Question

A standard 52-card deck consists of 4 suits and 13 ranks. Find the number of 5-card hands where any hand is allowed (namely the number of different hands)

Answer 1

Answer:

If you want the probability of getting five cards of the same suit, i.e. a natural flush, it would be 13C5 * (4! / 3!) / 52C5 = 5148 / 2,598,960 = .00198… or about 1 in 505.

If you’re asking the probability of having all four suits represented in your hand, it would be 13C2 * (13C1)³ * (4! / 3!) / 52C5 = 685,464 / 2,598,960 = .26375…

Step-by-step explanation:

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