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

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  • 3 years ago
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    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:

    http://www.mathsisfun.com/combinatorics/combinatio...

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