Combinations and Permutations Word Problems

[@TheJohnnyCombat]

What a teacher! Cheers mate! My kids think I'm brilliant! When they're older I'll tell them the truth!! All the best and keep doing great things!! Thank you!!

[@sourayeaturaye2498]

John Cummins lol

[@sakshyamranabhat8256]

What a dad

[@eyupcomez]

Man, i think some fathers are better than others. And you are good one 😂

[@tonybarfridge4369]

We all learn from someone else, unless we invent it, but then we are still using others' ideas

[@lisamullis7917]

Paid for a GRE prep course for the math portion. These videos are doing the trick instead! So appreciated! Thanks!

[@yourbuddy4676]

unfortunately, the first 2 problem are wrong. Don't know about the rest as I stopped watching after finding first 2 wrong.

[@thisisnotpaperhats]

when your teacher is a youtuber

[@nourhanhazem2402]

Since 2020

[@Supreme-Sharma]

Since 2022

[@yuruxgaming5790]

Since 2019

[@supermuslim8263]

Since 2024

[@omni7896]

Dude, I figured out how to do permutations and combinations just by looking at the thumbnail Also like if you're watching in 2019

[@baconmarine7985]

big brain gang

[@luker.6967]

There are harder problems than these.

[@davidthefifth]

2021 so im from the future aka the present

[@lifeless.sandwich]

Lmao fr

[@omni7896]

2021? Bet

[@thelittlechef6066]

I have not yet found anyone on the internet who explained this easier and better than you did!!! This was AMAZING!! Thank you sir!!

[@MechanicsStudents]

Felt like just the other day I watched videos on this channel to pass my algebra regents, now I'm doing statistics. Time flies.

[@gingermuro6388]

i still have no idea how to figure out if the order matters or not

[@brandon5058]

This was so perfect! You are amazing and yooooo, that accent is dope. :)

[@tecmath]

Thank you. Hope it helped

[@zephyr1327]

Brandon u mean the low pitched voice? Because the accent sounds like a normal American one.

[@ellichen6748]

it’s not normal american...more like australian or new zealander...

[@MUMTAZKHAN-up7pp]

A permutation is a set of all possible arrangements of some or all objects from the collection, when the order of the selection of objects from the collection is important. The combination is a selection of objects from the collection, such that (unlike permutations) the order of selection from the collection does not matter. For example, • Fruit salad of apples, grapes and bananas is a combination. If we do not care what order the fruits are in, then they could also be "bananas, grapes and apples" or "grapes, apples and bananas", it is the same fruit salad. • Selection of the five number of peoples for the team is a combination. You could order them by names, heights or something else, but essentially you would still have the same team, ordering is irreverent. • The ATM pin code “1234” is a combination. Now we do care about the order. The orders 4321" or "3412” would not work. It has to be exactly “1234” for opening the ATM machine. The languages that are more precise in counting techniques are the following: • If the order does not matter, then it is a combination • If the order does matter, it is a permutation

[@alfredoalzulaiii3168]

I love how you teach sir very brief yet so easy to understand

[@zephyr1327]

A seemingly difficult topic was very easy in reality! Thanks sir.

[@tecmath]

oh man...i'm only the third comment!

[@justinsantos5751]

Vani Ahuja watch his combinations video. It's because the formula for combination is n!/(n-r)!r! n is the number of items, r is the number of place or digits to be filled. For example: pick 3 supercars from 50 supercars. 50 is the n, and 3 is the r. That's for comvination.

[@eddeno9]

Lol its not a race

[@otegelilian6779]

Watching it some hours to exams and am greatful it has really help

[@cedrickdeguzman3997]

5:55 we answered that yesterday and Got the correct answer😀😀😀... Thank you for the easier step

[@xwavestr]

I could watch you write all day long. The numbers/shapes are so neat and natural it's mesmerizing... A big improvement from the horrendous oversized scratchy felt marker on paper *cringe*

[@mordom153]

Thanks for the extra comb and perm word problems! It helped me a lot on the math comps.

[@astoldbyashley9121]

Anybody else here the morning of a test and learned this literally within 5 minutes of watching?!! What is my professor doing?

[@gloriachomba7333]

Thanks alot darn a whole 3hr lecture understood in minutes... thankyou ☺️✅

[@yuruxgaming5790]

The schools need this guy

[@vhanessabautista9717]

The last question could simply be: Circular permutation, because it is talking about ( around a campfire).. anything that talks about circle use this. Formula: (n-1)! •how many ways can 6 people sit around a campfire? 6-1= 5! = 120 ways

[@moej.8228]

Sips Tea thanks hope it works on the test

[@nayanvaishnavvv]

Thanks dude!! Much ❤ to you.

[@thus.spoke.zarathustra]

There is a reason for this. For every permutation, you can rotate it and form another. So for n permutation, you have n duplicates. So you simply do n!/n which is (n-1)!

[@josepholuwatoni7202]

i think your voice made this easier to understand

[@fishhikeforage]

There's some confusion about the first example---tecmath is right, it is a permutation. Think of it as making a playlist. Keyword here will be "list". The order matters because otherwise it's a different performance, a different concert if you will.

[@yourbuddy4676]

No. If 3 songs are chosen, let them be A, B and C, and the order in which they are choose can be ABC, BAC, BCA etc. They are still the same songs just in different order. You can perform A, B or C in any order. Therefore, Order does not matter. It is a combination as ABC, BAC, BCA are same and has to be divided by 3!. Lets take your example of "LIST". Suppose u have 3 songs in a list, u can play them in any order so order does not matter. But If the question had specified that the song A has to be played 1st, B 2nd, and C 3rd then ABC, BAC, and BCA will be different (this is what u r assuming and what techmat assumed without specifying in the question) then it would be permutation. Moreover techmat swaped the methods of first 2 question (don't know about rest as I didn't watch). The second question has to be solved using permutation in which he used combination

[@st8tesman]

@@yourbuddy4676 This is a permutation because the order in which the songs are performed matters. In a permutation, different arrangements or sequences of the same items are counted separately. For example, if the person chooses to perform three songs out of seven - say, Song A, Song B, and Song C - the sequence in which they perform these songs is significant. Performing the songs in the order "A, B, C" is different from performing them in the order "B, C, A" or "C, A, B." Each different sequence represents a distinct arrangement, and that's why we use permutations. If the order did not matter, we would use combinations. In a combination, choosing the same three songs (A, B, and C) would count as one outcome, regardless of their order. But since the order is important here (performing one song first, second, and third creates different experiences), we treat it as a permutation. In summary: Permutations are used when the order does matter. Combinations are used when the order does not matter. Since the problem involves performing songs in a particular sequence, it's a permutation question.

[@mainel6486]

Still confused about when order matters vs when it doesnt matter.... can anyone give me a trick to determine when it matters and when it doesnt?

[@shadycat_1935]

For the campfire problem, you could have set one person as the reference point, and the rest is a factorial. 5!= 120. This is an easier method imo!

[@tecmath]

I like it!

[@gamer3928]

1:40 they've already sung one the songs in this spice hiya

[@calfpv5973]

For the first question surely you need to divide by 3! to take into account the different orders of songs? 210 ways includes 3! ways of doing the same 3 songs just in a different order?? Then for second question, surely you would NOT divide by the 3! because giving 1st and 2nd and 3rd in a different order means giving different horses different places - order IS important here so you DON'T divide. Am I reading the questions wrong and going crazy here or are your permutations and combinations a little muddled???

[@brbmgmb7945]

so true. :( I'm also getting wooho crazy

[@lavionssoul5240]

I agree

[@cuteko713]

I think this video is wrong ;(

[@rainawhite8014]

For the the 1st question i believe he left off that you should divided the 210 by 6 which will give you 35 ways since it is a combination problem. If you were to check it on your hand held calculator you can do this. Calculator functions: press MATH go to PROB press nCr then enter the nCr His answers for 2 and 3 are correct, but I'm unsure about question #4 with the MISSISSIPPI since i got lost myself. Just a suggestion if this video confused you and did not help you to get a better understanding i feel you should try this one instead kzbin.info/www/bejne/jmqQip2uqZuhnJY&pbjreload=10 i think he breaks it down better.

[@Ra-tu8rj]

Pretty sure that on the first question, you need to do 7 3 NCP, since the order doesnt matter. and for the answer you will then get 35. so yeah, he is wrong

[@keysi4967]

This was the easier one but my teacher gives us the harder one with solutions. Well thanks for tgis

[@sofiaabod9326]

In the first question, why is it you used permutation? The problem is not in order it must be combination. Am I right?

[@gigistarlight]

I WAS ABOUT TO COMMENT THIS!! I'm so confused as to why he did that.

[@cloydniere6838]

Same here :((

[@buddylove557]

I think it's bc it 3 specific songs to perform ...not sure though I'll look more into it

[@heartfieldlamadrid8187]

It should be combination

[@slashie.]

@@heartfieldlamadrid8187 think of it as no song should repeat which is why it became a permutation question

[@spencerjames9417]

You explained this so clearly!

[@Mona-mu5he]

U MADE THIS FREAKIN PROBABILITY VERY EASY

[@lesliebassett8168]

OMG I am lookning at helping my son with MQM 100 and I actually understand this by the way you teach I am like it can't be this simple ?

[@JannisAdmek]

I love these videos, keep 'em coming

[@charankawal1548]

I like your style. Thanks very much for sharing

[@fireflies15]

This is very helpful and the examples are excellent. Thank you

[@shamelamaetumala7032]

I don't get it at all, but I think there's something wrong there. I'm glad that I read the comments. I knew something was up. I just couldn't figure it what or why.

[@ihaveseverefrootsnackism]

I can't tell if I'm here more so for the advice or the Australian accent.

[@tecmath]

The accent.

[@VWabhijit]

Why does the order matter when you're sitting around a campfire?

[@roldanrapallo7991]

1. Write a program that accepts an integer input from the user and display the least number of combinations of 200s, 100s, 50s, 20s, 10s, 5s, and 1s. [Test your solution using this samples] a. Input: 250 Output: 1x200s, 1x50s b. Input: 1127 Output: 5x200s, 1x100s, 1x20s, 1x5s, 2x1s c. Input: 1127 Output: 5x200s, 1x100s, 1x20s, 1x5s, 2x1s d. Input: 19 Output: 1x10s, 1x5s, 4x1s [Hints] o Use division to determine the number of occurrence of each element (i.e. 200, 100) in the input (e.g. Given 500 if we divide it by the largest number possible; which is 200; we will get 2. Therefore, there are 2x200s.) o Use subtraction to determine the remaining value of the input. (e.g. In the 500 example, since there are 2x200s, we still have 100 to process. The 100 came from 500 - (2*200) = 100.) o Use the next largest number possible (i.e. 100) to check the number of occurrence. Continue until the remaining value of the input is zero. pls help me

[@SofiaChen-fm1se]

for the camp fire question, why it is divided by 6 but not minus 6? I'm still confused.

[@sqfx744]

It's not just the six similar positions he showed. For every possible arrangement there are 6 redundant positions. Does that make sense? Consider his example but switch two people. Now rotate them. You will find 6 more redundant positions. This means you need to divide the total number of arrangements by 6 redundant positions for every arrangement.

[@mitsukianzai9874]

I'm 'bout to fail my class 💀

[@3ckortreat]

Why order matters when singer gonna choose songs to sing? Anyway he will sing 3 of them, doesnt matter which one is first or last

[@TokyoXtreme]

Are you suggesting that song arrangement on an album or a concert set list isn’t important?

[@vemkatveera8981]

you explained it very well superb

[@kyuu6536]

Thanks i feel as if i know 100% now !

[@Qhawe189]

Can you please explain it in details I do not see why and how you cancel the numbers when multiplying.

[@future2339]

Dude..... The Mississippi one had me ⚰️ Went over it 6 times and still don't understand it

[@tonybarfridge4369]

That is the total different permutations or anagrams of that word using all the letters. What they never explain or mention is part permutations. What if u want to know how many permutations of 4 letters can be made from that word? Pretty hard writing them out by hand. So what is the math solution? I can tell u there are 11 different 1 letter words, and 34,650 different 10 letter words. That's it.

[@jomonjoshy8406]

There are 11 alphabets so 11!.. And there are 2 p's, 4 i's and 4 s's ..These can cause duplicates when we arrange the word MISSISSIPPI. So we divide with 2!*41*4! and thus duplicates are not created.

[@joebenge7420]

Great video, but I wouldn't agree with the last one in assuming that rotating them doesn't count. If we wanted to assume that it should be in the wording, not the explanation.

[@ismailerenkaraca4881]

I cant be the only one thinking that you sound like Jeremy Clarkson!!

[@ryym5913]

Your letters are cute. I love it

[@cheslyntesoro7153]

Thank you so much😊 It helps me a lot

[@Tomahawk1999]

Similarly the second question solution is wrong, that is NOT a combination but a permutation problem. 3 horses are chosen for 1,2,3rd positions so ABC is not the same as BAC or CAB. correct answer is 12 x 11 x 10 = 1320 and not 1320 / 3 ! which would be the no of all possible ways 3 horses could be chosen from a group of 12 horses.

[@Calverkristina]

Hello, thank you for a great video. I have a question about the final problem. How come there are 6 ways of ordering the group of people the same way, rather than 5? I thought that once the person returns to their original seat then this change shouldn't be counted as it is the same (eg ABCDEF returning to ABCDEF, as opposed to the other similar cases like BCDEFA) Thank you in advance

[@MyBigThing2010]

Am I the only one who HATES these and when I think of Hell I picture a math professor handing these out at a unsolvable rate.

[@littlemanhuerta4442]

Teachers are stupid teaching us how to do it the hard way its like they want us to have bad grades

[@alfredoalzulaiii3168]

That's right and they are

[@notalentgamer3384]

Doing it the hard way is more of like a 2-way street, it can be good, ooor it can be bad... But this is my opinion on the matter anyway.

[@TheTriangle444]

the problem is teachers teach us the literal barebones of the lessons and they want to call it the "basics" then make some stupid crazy wonder questions in the test papers... i suppose students got to study longer in home than school

[@alexismandelias]

Well... first of all, it's*, learn to speak English. Also, do you even think before typing?

[@geraldmorales2091]

lol our teacher literally include the problems in our quizzes which are meant to be taught to us a week after

[@victoriamichaels6930]

I couldn’t get past him sounding like the Geico gecko 🦎

[@stevencaruso825]

The first question suggests that "the performers will perform 3 songs", so this is not a normal permutation, where the null set and sets containing 1 & 2 elements are valid.

[@silverbowftw5225]

So is he wrong?

[@lovelynorabe2020]

Thank you beybeh

[@anja5545]

In a restaurant the first dish costs 0.80 euros ,the main dish costs 2.40 euros and the dessert costs 1.20 euros.3 friends ate and paid a total of 10 euros.Each of them ate at least 2 out of 3 dishes.How many first dishes,main dishes and desserts did they buy?

[@Rayan-wo8zt]

Integration and differentiation is far easier than counting😓😓

[@ijeomaisaac254]

I don't actually understand it as well as expected

[@Mona-mu5he]

U R AN AMAZINGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG TEACHER !!!!!!!!!!!!!!!!!!!!!!!

[@martinduggan4077]

This beat me But love the channel

[@kevinpari9500]

chill dude, good math :)

[@MathsPathShala1729]

Nice way of explanation... 👍🏻 #MathsPathshala

[@vergelgundran7486]

What happened to the last question??? Why did you divide it by 6?

[@pawelpow]

Same! I'm confused

[@ynnagesite5678]

Vergel Gundran becaause the formula for circular permutation must be divided on its n

[@marinamuller2385]

Thanks for this video! Just one question, what’s the difference between the first exercise with the songs and the third one with the cards? Why is the first one permutation and the third one combination? In other words, why does order matter in the first one (since it’s a permutation) and it does not matter in the third one (which is a combination)? Thanks in advance and thanks for the great video!

[@xXDamolaXx]

I guess with songs the set list does matter!

[@fathimarifa507]

i think its a permutation in both cases. many times the only difference between going w perm or going w comb is just the way the qn is worded. both mentioned "different ways" in which the objects could be chosen, meaning order does matter. and usually, combination is calculated on qns where the objects are indistinguishable, like say choosing 2 out of 5 green balls. clearly, it doesnt matter which ball you choose first there.

[@kiethbernaldo9082]

I think the answer on the 2nd last question is 30 bcoz 3 and 2 can be divided by 6 in which in ur case you did not compute intirely and if the answer is really 15 then how come the number 3 below in being canceled? Nice vid though very helpful and educational.😊

[@laurenlemus6432]

For the Mississippi Question you forgot to consider there was 1 M . You only accounted for the P,S, and I .

[@Samueljack272]

I know I’m 1 year late but M is not a identical component that’s why he did not account for it.

[@allegory6393]

Thank you for this. I still don't understand why in example 5 ('How many different ways can 4 fruits be selected from 6 for a salad?') The top number order stops at 3 and does not go all the way to 1 (6x5x4x3 instead of 6x5x4x3x2x1). I'd be grateful if anyone could explain why this is the case.

[@russtorque2993]

That's all very impressive. But the 💲64, 000 question is: what can u do with those permuations & combinations in everyday life?

[@johnoommen8383]

no one cares dude

[@Peaknerd3]

What a life saver

[@EducationSearchers]

Good work

[@lavionssoul5240]

Actually for problems involving circular objects have this formula (n-1)!

[@life_choppa]

thanks ...

[@RaynerDaCruz]

Why is the last example divided by 6? If its a permutation, shouldn't it be 6!/(6-6)! == 6!/0! == 6!/1?

[@chenadam6339]

i think because its six people choose six seats, the permutation is 6!/(6-6)! and he just omitted it for simplicity. and since six people sitting in a round table, there are six specific arrangement. so you need to divide by six.

[@SolidSiren]

I have a question: The first question about songs. You did not include a factorial denominator, why? It seems to me that order DOES NOT matter in this question just as question 3 where you DO include a factorial denominator. How are "cards dealt" any different from "songs performed"? The order is irrelevant in both cases, you end up with a group of 3 or 5. What is the difference, please?

[@adengoher4343]

Thank you!

[@mattrivera2429]

Can so.eone awnser me, WHEN DOES THE ORDER MATTER. I know how to calculate it I just don't know which formula to use because I can't tell when the order matters

[@lillianp8900]

you can solve these also by using the prb button on your calculator.

[@keym3955]

Yaaaas boss~! So clean!

[@MonicaMLBH]

Why does order matter in the “Mississippi” example, but order doesn’t matter in the “deck of cards” example? The questions seem similar to me.

[@zb1blooming]

Watching as my final test for grade 12 is in 2 days

[@zakp8687]

for the last problem why did we divide the factorial of 6 by 6? for the other permutation questions we divided by a factorial, why was this not necessary for the last problem?

[@tecmath]

+Prince of Puntland permutations in a circle. If I wanted to arrange 4 objects I can do it 4! ways (24 ways). If the 4 objects are in a circle they can be arranged 4!/4 ways....we divide by 4 because the rotated arrangements are considered to be the same. 24/4 = 6 ways. Unsure still...look at the last problem in my permutations video ( link to playlist is included in the description of this video). It should help.

[@edwimo1966]

tecmath but what is it wasn't a permutation in a circle For example the guy on the top of the camp fire goes at the place of the guy under the campfire Does ur technique still work?

[@lasnybrat8978]

The explanation on 4:35 was rather vauge, better to precise that combination i.e. the order of the chosen horses doesn’t matter but the set of horses does matter

[@MaxDoesFitness]

I don't understand why you have to divide it, why couldn't you just leave it as 6x5x4x3x2x1 for example?

[@ghostfromcod7752]

we are close to 1million subs

[@cyan1153]

Why is third question with the card a combination? Shouldn't the order matter because we can have one card be in the 4th position or the in 7th position?

[@cyan1153]

Ohhh wait nevermind I read the question incorrect mb lol

[@Teabonesteak]

Spot on videos!

[@Venom-dg7jt]

I’m literally still confused I mean for the first ex I kinda understand that you rlly can’t play the same song 3 times but then again you can do that. It’s like this question I have for hw, 8 ppl apply for 3 different jobs at a company. I mean it kinda sounded like a permutation but it rlly doesn’t matter who gets what job. Or idk. Can someone help me understand cuz I’m super unsure

[@shadycat_1935]

Def not an expert myself, but I'm going to try to help you out a bit (albeit a tad late innit). Think about it this way: there are 8 people applying for 3 different jobs. It helps to think like he did, with underlines. Three jobs, so three underlines: _ x _ x _. In the beginning, there are 8 people who can get the job: n(ways 8 people can be hired for 3 jobs)= 8 x _ x _. Now, the first person hired can't be hired again, which means there is one less person available: 8 x 7 x _. The first person and the second person hired can't be hired again, so we have to subtract 2 people from the total candidates available. That leaves us with 8 x 7 x 6 = 336. There are 336 ways 8 people can be hired for 3 jobs. The problem is a permutation cause the order matters, aka the same person can't be hired more than once. A combination is when the order doesn't matter. Hope this helped!

[@linhsu7549]

i dont get it

[@swiftsifu]

There's an error at 5:52 the answer is 311,875,200. You've done 52*51*50*49*4 you missed the 8 at the end when calculating.

[@nathanvemulapalli2]

in how many ways two books on five shelves so there is not more than one book on a shelf? If the books are identical, then there are ways. If the books are all different, then there are ways. how to do this?

[@annaakopby8829]

So is #2 a permutation? Did not make that clear.

[@MonicaMLBH]

Disregard; I see the difference. Order matters in the “Mississippi” example because there’s only way to spell the word Mississippi, so it matters where the duplicated letters are placed.

[@Tomahawk1999]

The first question solution is wrong. It is not permutation but combinations because song list ABC is the same as song list BCA. It is a group. answer would be 7x6x5 / 3! = 35. 210 is the no of permutations but thats meaningless given the context of the question which is to perform 3 songs out of a total of 7.

[@kylewc2286]

i agree

[@powerpuffmuse847]

Thank you 😘😆😉

[@hi_238]

Why on the song question, You didnt divide anything?

[@RHSkmg365]

What if I have 3 styles of mashed potatoes and can be cooked in 3 different textures, and can be flavored 5 different ways, how many ways can I order my mashed potatoes?

[@MuhammadAli-bp6iq]

Horse A B C can win C A B or B A C. Where I’m wrong. It’s permutation not combination.

[@ehyyouwelcom]

the mississippi question it's 4194304 ways

[@Rakatashii]

this was helpful ty

[@dasartattack]

Last question I did not get

[@nicosoftnt]

So, if the problem was about "How many ways can 6 people ordered in line", the problem would be pretty easy. The answer would be 6! (also known as) → 6 x 5 x 4 x 3 x 2 x 1. Now, since the problem includes a table in which the people sit around, the conditions change. Imagine each person has by name a letter. First person "A", Second person "B", Third person is "C", Fourth person is "D", Fifth person is "E" and the Sixth person is "F". If there are 6 spots (one spot for every person), and A is sitting next to B, who is next to C and so on... you could move the entire group one spot (Imagine you grab the 6 of them and change their spots at the same time) such as A still sit next to B, and B next to C and so on... You moved the whole group and didn't at the same time. Now, how many times can you do that? , one time per person/spot. That means, there are 6 times in which everybody are in a different spot, yet in the same order. Well then you have to divide 6! by 6. That is 720 by 6 which is 120.

[@SofiaChen-fm1se]

@@nicosoftnt why not minus 6?