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

Question

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?

Answer 1

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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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