Poker Hands

Robert S. Wilson

This is covered in Math 131 and Math 300

Type of Hand

Computation

Number

Royal Flush

4

4

Straight Flush

9x4

36

4 of a Kind

13 x 48

624

Full House

13 x C(4,3) x 12 x C(4,2)

3,744

Flush

4 x C(13,5) - 40

5,108

Straight

10 x 45 - 40

10,200

3 of a Kind

13 x C(4,3) x 48 x 44 /2!

54,912

2 Pair

13 x C(4,2) x 12 x C(4,2) x 44 /2!

123,552

1 Pair

13 x C(4,2) x 48 x 44 x 40 /3!

1,098,240

Nothing

52 x 48 x 44 x 40 x 36 /5! - 15,348

1,302,540

Totals

C(52,5)

2,598,960

7 card hands

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