How Many Ways to Split Students and Combine Outfits?

[Apophis]

I can normally do combinations and permutations, but these two currently stump me. Any help is appreciated.

1) Twelve students are in a class. They are split so that five go to room A, four go to room B and three go to room C. How many different ways can this happen?

2) You have six pairs of jeans, three shirts and two pairs of sandals. How many different outfits can you wear from these choices?

 

[whozum]

For number two, I think (2c1)(3c1)(6c1) describes the correct answer. There are 36 combinations. Thats evaluated as

nCk = \frac{n!}{k!(n-k)!}

 

[Dr.Brain]

For The First One:

(12C_5)(7C_4)(3C_3)

For The Second One:

Take One Shirt ===> You can pair it up with 6 different jeans
And each of the above pair of shirt+jeans can be worn in two way (with 2 different pairs of sandals) Therefore total cases=

(1 x 6) x 2 =12

Similarily the above case happenes 3 times for three different shirts :

12 x 3

Ans= 36

 

[Apophis]

Thank You

Thank You all for the help. This makes more sense to me now.