# Homework Help: Poker 10 Decks, 10 cards, independent 4 Aces

1. Nov 11, 2006

### mattmns

Silly question of very little importance

My dad just asked me the following question: You have 10 standard independent decks (52 cards), you draw 1 card from each deck 1 at a time, what is the probability (count) of getting 4 aces (not necessarily distinct suits) out of the 10 cards you draw.
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I am thinking that the number of ways to get such a "hand" of 10 cards is the following:
$$\binom{10}{4}\left(\frac{4}{52}\right)^4\left(\frac{48}{52}\right)^6$$

Reasoning being that you want 4 aces and there are 4 per deck, hence the (4/52)^4 and for the other 6 cards you want you have (48/52)^6, then 10 choose 4 for all the different ways you can get the 4 aces out of the 10 cards.

And if we wanted the aces to have distinct suits we would have 4! instead of 4^4

Does this look correct? Thanks.