# Drawing ten cards from 52 cards

1. Oct 2, 2011

### KFC

Hi there,
I am thinking a question from a book about drawing ten cards from 52 cards. The first case is drawing ten cards, having 7 cards of a club, 1 card of a heart, 2 cards of a diamond. The order doesn't matter, so the total number of possibilities is

C(13, 7)*C(13, 1)*C(13, 2) = 1740024

In the second case, if I need to draw ten cards, having 8 cards of a club, 1 card of a heart, 1 card of a diamond, so the total number of possibilities is

C(13, 8)*C(13, 1)*C(13, 1) = 217503

but I was told that for the second case, the answer should be 117117. Do you know how they get the number 117117 or in what case will this number come up?

2. Oct 2, 2011

### Bacle

from is by factoring it:

117117=7.9.11.132 , sometimes that helps reverse-engineer the answer.

BTW, I love the new snackers and the extra-crispy recipe. You're still doing it right.

Last edited: Oct 2, 2011
3. Oct 3, 2011

### KFC

Thank you for your hint. I was told by someone that though C(13, 8)*C(13, 1)*C(13, 1) is a right number, but 117117 may be used by some card simulator. I am thinking the 13*13 is the way to deal one heart and one diamond, but for the first three number 7, 9 and 11, I still confuse how this three numbers associate to deal cards of club.