Permutations With Restrictions

[@Qwwer1123]

Never knew that a 15min discussion would be better than listening to my prof for an hour..ty

[@ttvurmom6185]

I’m using this to prepare myself for the Mathletes Competition on November 16. It’s only 32 days away. Thanks for the vid! May God bless you.

[@najminevlog6797]

TTV Ur Mom goodluck

[@sampsonekwet5497]

How did you do?

[@Jerome-n4l]

how did u do

[@sylvestermainoo8851]

Thanks so much. This was so helpful and your explanations were easy really easy to understand

[@yona1479]

Thanks so much!! This helped me a lot plus your explanation is great!

[@prabhatshuklaofficial5228]

I understood this concept very nicely sir.

[@glebkozlovskiy1101]

isnt the first one su[posed to be 4 factorial?

[@AlRichards314]

He's selecting 6 cards at a time, so that's why the numerators are 6!. The first one shows the number of ways there could be 4 blue and 2 red, so we get 6!/(2!4!). The second one shows how many ways there could be 3 red & 3 blue, hence why it's 6!/(3!3!). Hope that helps.

[@ironmason]

Hello! In 2C, why 5xP(7,4)? I thought i should be P(7,4)^5, (read as raise to 5). Thank you!

[@AlRichards314]

Hey. The reason for the x5 in 2c is that there are just 5 different positions for the letter "U". Think of this as P(7,4) ways to arrange the other 4 letters, then x5 since there are 5 places the "U" can be placed. Hope that makes sense.

[@ironmason]

@@AlRichards314 Oh! Now I understand! Thank you! This will be a good reference. I was thinking about 5 unique numbers from 1-15. How many will be if all 5 numbers are in sequence.

[@danillejoycarcueva9054]

What if it says how will she be seated if they have to be seated one seat apart

[@AlRichards314]

Let's say it's Joe & Lisa (J & L) plus 6 other people. The easting will look something like this: J _ L _ _ _ _ _. There are 6 ways that cn occur down to _ _ _ _ _ _ J _ L. This 6 is the same as the number of other people. So there will b 6! x 6 x 2 ways for this to happen. The 6! is the number of other people and the 6 is the number of ways they can be one east apart. The x2 is because it can be J _ L or L _ J... Hope that make sense.

[@ToHereCan]

If you do P(6,6) for 3b then why don't you do 2 x P(7,4) for 2d by treating TH as a single object?

[@ToHereCan]

Is it because if you do 2 x P(7,4) it doesn't guarantee that TH or HT is in the word?

[@AlRichards314]

When you use P(7,4) that's an arrangement of 7 object taken 4 at a time, So any 3 of those objects will not be in the arrangement. Question 3b says the T and H must be in the arrangement, so it's a lot like 2b. Notice that 2d's answer is just 2b's answer times 4x2.

[@souaadatwi6936]

In 3_b why we didnot multply by 6 for places

[@AlRichards314]

The P(6,6) which is 6! accounts for the number of ways to arrange 6 things, which is 1 couple and 5 other individuals. The x2 is because any 2 people can sit in 2 different ways. On the left of the pair or the right.

[@souaadatwi6936]

Okay but why in the previous example he multiply by 4 for places of th

[@souaadatwi6936]

I mean what is the differnce btw 2_d and this part

[@yashpawse4690]

Clear and understandable! Thanks.

[@ShinEKMG]

Wow. This is very great explanation!

[@arjo6505]

I understand it better than my math teacher...

[@aimeeuwase1172]

On number one would it make a difference if the balls weren't identical

[@aimeeuwase1172]

I mean the cards

[@Ulttleshjt]

P(6,6) explaination could use some work

[@AlRichards314]

What I was trying to explain was that the 7 people is really one couple that are always together plus 5 other people, so there are 6 'things" to arrange, hence the P(6,6).

[@PM-vs3rh]

AlRichards314 but don’t TH also work as a couple? You didn’t have that as P(7,4).

[@manyaldwin3088]

I’m stupid I don’t know how you would get 6 in b

[@AlRichards314]

Hey. Don't be so hard on yourself. In example 2 b) SOUTHERN has 8 letters. If you take the S & N out there's only 6 letters left that you can put in the middle 3 spots. So the P(6,3) is 3 letters from O,U,T,H,E, and R, which is 6 letters.

[@manyaldwin3088]

@@AlRichards314 thanks I think I got the gist of it now thanks again

[@kongking1180]

thank you sir im about to take an difficult exam tomorrow

[@heyitsjay3686]

lol same, mines tomorrow as well

[@edoukouemmanuel2424]

Understandable🤗

[@jahilterox6015]

thank youuuuuuuuuuuuuuuuu...omg this chapter so cnfusing

[@saintyop123]

other way for the first question: 7A6 / ( 4! * 3! )

[@ttvurmom6185]

Youssef Mankari, 5040/144 = 35. You are right, however I think he is trying to explain for lower leveled kids.