## Monday, August 22, 2005

### Poker Hand

Two part question,
How many different hands are possible in a 52 card deck?
Given that, what's the probability of getting four aces?

I think this is a good question, given how popular poker is right now. Anyone have any good stories or links to share about poker strategies?

#### 1 comment:

1. This is similar to yesterdays question, in that we have 52 cards, and we are choosing 5. So the solution to part 1 is: 52 choose 5 = 2,598,960

The probability of getting four aces is the number of ways you can get four aces divided by the number of possible hands. There are 48 possible hands where you have four aces. <- Since you have 4 aces, you can only fill in the last card with the 48 other cards. So the probability of getting four aces is 48/2,598,960 = 0.00001847 or about 1 in 50,000!

So the next time you get four aces, treasure it, it probably won't happen again anytime soon!

To find out more, search for equally likely outcomes, n choose k, and probability theory.

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