# Combination of 5 cards given a 7 card set

I haven't done a whole lot of maths since uni and cant remember the equation for this. What I want to know:

Given 7 playing cards, how many 5 card combinations are there from this set?

This is a poker maths problem.

e.g. So given the player has [As, Ac] in his/her hole cards, on a board of [3s, 2c, Kc, Js, Qh]

How many 5 card cominations are there? eg As, 3s, 2c, Js, Qh

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## 1 Answer

In general, you can pick 5 cards out of seven in $\binom{7}{5}$ ways, where $\binom{n}{k}=\frac{n!}{k!(n-k)!}$.

Hope this helps.

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This works out to 21 combinations. Learning a bit about combinations will help you solve other problems of the same type. –  Austin Mohr Aug 13 '11 at 19:44
Yes, i forgot to calculate the result... –  Beni Bogosel Aug 13 '11 at 19:45