# Statistics problem?

I really need help with this question because I am completely lost. Thanks!

1. What is the probability of getting an ace, a king, and three of a kind in a five card poker hand?

### 1 Answer

- SamwiseLv 73 years agoFavorite Answer
I take it that the three of a kind are not aces or kings, then.

So there are 4 possible aces,

4 possible kings,

and 11 possible ranks for the three of a kind,

which can have any one of 4 cards of that rank not included.

That gives us

4 * 4 * 11 * 4 = 704 hands that fit this description.

There are

52C5 = 52! / (47! 5!)

= 52 * 51 * 50 * 49 * 48 / (5 * 4* 3 * 2 * 1)

= 52 * 51 * 10 * 49 * 2

= 2,598,960 possible 5-card hands in all,

so the probability is

704 / 2,598,960

= 44 / 162,435

= about 0.00027

I've used a combinations formula here.

If you need any help with the use, derivation, or calculation of such formulas,

I highly recommend this online tutorial: