[Discrete Mathematics] Rule of Sum and Rule of Product Examples

[@stevenparson1727]

Mr Trevor, I greatly appreciate your videos. With regards to the president + female vice president problem, I believe you've presented an unnecessarily complicated solution (probably to demonstrate the idea of separating a problem into cases). For this particular problem, an easier way is to choose the vice president first (1 of 8 females) then the president (1 of the 12 remaining candidates). 8 x 12 = 96.

[@freshmilk7122]

Wow! Idid not thought of that

[@Engkk]

mind blown

[@nearobserver29]

oh thanks bro :)

[@Deksudo]

wow. makes sense.

[@daroxz3889]

5,400 feels a little extra. If I selected meat A, B, and C it would essentially be the same as B, A and C right? So would combination not be a better fit here? Appreciate the great video

[@danlabrador]

True

[@airamae1099]

HI sir, why did you used persmutation in the sandwich problem and not combination? Whichever set of meat and cheese you get, it'll just be the same sandwich thank you for this video tho

[@PureAndAppliedMath]

Hey, the last part is somehow incomplete! You made it in order. The arrangement of meat and cheese doesn't have to be ordered!

[@TheMountainBeyondTheWoods]

What are you even talking about? How is it somehow incomplete and why do you care what order he put the cheese and the meat?

[@PureAndAppliedMath]

Hey @@TheMountainBeyondTheWoods , am not criticizing; am just "commenting." Yes, he should have used combination instead of permutation.

[@zacharyhe5719]

the last question, 3 meat 2 cheese sandwich, my answer is 450, because the order of meat should not be concerned, so do cheese. your solution consider the first meat and second and third, there is no relation with order, I think :)

[@jimhorng]

+1

[@bobblebee49]

Yeah order shouldn't matter! how did you account for this?

[@lanehensley9948]

@@bobblebee49 Hey Brad, I got 450. Here's how: you start with the bread 3. Then you times it by the amount you get from all pairs of 3 meats using this formula (5!/n(5-n)!) where n is the size of groupings (3 is the size we want of each group of meats) so placing 3 inside the formula you get (5!/3(5-3)!) = (5*4*3*2!/ 3(2!)) = (5*4*3/3)= 20. (Keep in mind that x!/x! cancel each other out!) So there are 20 no repeat of groups of 3 meats. You can apply this formula to the cheeses as well and you'll get (6*5*4!/2(6-2)!)= (6*5/2) = 15. multipy it all and get: 3 * 20 * 15 = 900. But this in it's self give you repeats! I overlook this at first... so you will divide by two to 900/2 = 450. Here's a simple example of why there are repeats at the end: lets say you want to know all pairs out of a set {1, 2, 3, 4} well you could do 4*3 and get 12 but here's the 12 pairs: [(1,2) (1,3) (1,4) (2,1) (2,3) (2,4) (3,1) (3,2) (3,4) (4,1) (4,2) (4,3)]... but wait isn't (1,2) and (2,1) the same? In the case of dealing with sandwiches they are because order isn't a concern. so we divide by two to give the first half of the pairs.

[@USMANNDEV1]

plzz tell me how first have solve??

[@ElshanVideo]

This was so good, Thanks!

[@loubenedicvalle524]

I highly appreciate the videos, Sir, since some topics I have to teach in my Discrete Structures for Computer Science are here. But I think the meat and cheese problem should have used the combinations since the order (arrangement) of order (query of food) is not required.

[@cxldblooded4307]

I thought the same thing good to see that Im not crazy

[@zahinarman24662]

I KEEP FORGETTING TO LIKE THESE EDUCATIONAL VIDEOS, I JST KEEP WATCHING FROM PLAYLIST AND JUST MOVE ON TO THE NEXT WITHOUT LIKING

[@husseinkhalil5023]

How do we know what no repeat means. In those 5400 sandwiches there is always 3 differents meats in each sandwich but a lot of the sandwiches have the 3 same meat combination... they're only in different order. I thought of it as a practical "no repetition" when i first red the question. Restaurant don't sell sandwiches with the same meat but in different order and call them two different meals.

[@imdoug]

You sound like the narrator from the TedED videos

[@camishere4584]

Nah, more KhanAcademy

[@elizeallen6613]

How do you use the product and sul rule wheb with 2 heterozygote fruitflies with 1 having Cc and one having bb eye color

[@jasonsourivong4303]

In the first question of (iii) where did the remainder of 7 come from?

[@victoriaahmadi577]

How many strings from decimal numbers does it exist of length 4 if exactly 3 of them are the same?

[@persianhenry2897]

I hope this helps. If the same number, lets say is 9 then we would have something like this. *999 9*99 99*9 999* now the * represents numbers other than 9, that is numbers from 0 to 8 which is all together 9 possible options. So 9 * 4 = 36 (provided the the same digit is 9) since there are 10 decimal numbers, the total strings would be 36 * 10 = 360

[@jaysmith4302]

In the last example, why isn't it 5 choose 3 and 6 choose 2?

[@Trevtutor]

+Jay Smith The meat is ordered in this example, just not written as such. This is prior to combinations being introduced, so the idea is to just use what I've presented so far. If we're being realistic, then yes, it's probably (5C3)*(6C2) for those.

[@EntertainmentUnit]

Does this mean that the answer in the video considers a sandwich with roast beef, ham, and salami a different sandwich than one with the same meats in a different order?

[@mbarq2]

Yep! You can try it with just three meats and pick two out of them to test it out (3 choose 2, which equals 3). Had you done it like in the video, you'd get 6 different combinations, where ham/salami and salami/ham are two different sandwiches! The only thing the "formula" in the video does is make sure you don't end up with a "salami/salami" sandwich (i.e repeating meats!)

[@thisiswhoiam7249]

For 2nd Q (ii): Am I wrong? (5C3) * (6C2)

[@airamae1099]

i agree

[@volo7]

wouldn't the president example with female vice be: either 13*8 or 13*7 since the first pick can be either male or female?

[@koober_]

That's what I got as well, but this answer gives 195 (13*8 + 13*7) while the one in the video gives 96. Can anyone explain why this is wrong?

[@Trevtutor]

You have to do it by cases. Male Pres * Female VicePrez + Female Pres * Female Viceprez

[@koober_]

Ah I see now, thanks for the quick reply. I just happened to unluckily choose from the total instead of from the males for both cases.

[@oxygen2671]

I don’t know I feel there is something wrong with the sandwich problem . In the first part shouldn’t it be the number of the way of the meat sandwich plus the number of the way of the cheese sandwich

[@seyiojewale7907]

i wonder if you study any of the hermetic material, this first example seems pretty insightful.

[@RalphMartinez007]

Hi Greta videos- can you direct me to valid/Invalid arguments explanation thank you!!

[@RiriTaw]

Isnt there a video where u explain sum???

[@Shreya-uc4lp]

bruh im getting severe high school data management flashbacks.......i wish i payed more attention in class back then.....

[@Bleachiiigo]

Seriously i don't hate descrete mathematics but i hate sum and product rule

[@sumbalkhan9902]

i don't understand the last example

[@sumbalkhan9902]

why you multiply with 3 in start in last video in both cases?????please answer me

[@itsnotdarien]

a sandwich is made from bread, there are 3 types of bread

[@zafarhussain8273]

why you choos eassy example

[@jankipatel2392]

Sir , a sandwich has 2 breads so the answer of the first question is I thik 3*5*6*2

[@MonsieurGilbert]

by your logic it would actually be 3*5*6*3, but he uses the same type of bread for top and bottom, so it would be 3*5*6.

[@nikolap5983]

shouldn't it be 2x3 for the bread, because there is a top and a bottom in a sandwich?

[@mustafaceylan597]

or you can choose the vice president first then choose the president

[@lourier3]

Your health would be better if you didn't eat so much meat and cheese.