Among the 2,598,960 possible 5-card poker hands from a standard 52 card deck, how many contain at least 1 spade?

Question

Among the 2,598,960 possible 5-card poker hands from a standard 52 card deck, how many contain at least 1 spade?

2 Answers

Answer Question

Answer 1

11, 830 possible hands with a spade. Oh and their are only 19,600 possible hands. Your number assumes that order is important, but in cards it isn't.

The following two hands are identical:

AAKJQ / JQAKA

These two hands are not treated as different combinations. So the total number of combinations is MUCH lower.

(I had to use some heavy math to solve this. HINT: It requires adding numbers called as Triangular Numbers. This is how you determine unique combinations.)

Answer 2

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