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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