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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?

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# Drawing ten cards from 52 cards

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