DISCRETE MATHS HELP!! How many Poker (5-card) hands consist of a.please EXPLAIN!?

How many Poker (5-card) hands consist of a "flush"

(i.e. all cards of the same suit)?

How many Poker (5-card) hands have exactly 3 Aces?

1 Answer

  • 7 years ago
    Favorite Answer

    If you want the number of choices of m different cards chosen from

    n different cards it is n!/(m!(n-m)!), where n!=1x2x3x...xn.

    1) For each suit you are choosing 5 from 13,

    the number of choices =13!/(5!8!)=1287

    There are 4 suits so the required number = 1287X4=5148 hands

    2) There are 4 aces and 48 not-aces.

    You want 3 choices from 4 = 4

    with 2 choices from 48 = 48!/(2!46!)=1128

    So total =4X1128=4512 hands


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