Drawing ten cards from 52 cards

[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?

 

[Bacle]

Your answer seems fine to me. One way of seeing where the answer may have come
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.

 

[KFC]

Your answer seems fine to me. One way of seeing where the answer may have come
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.

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.