FRANKJUVAL ORIENTAL RUGS OF DISTINCTION

Five Hand

A five card poker hand is dealt from a standard deck. Find the probability that the?

A five card poker hand is dealt from a standard deck. Find the probability that the hand is three of a kind (ranks a, a, a, b, c).

Out of C(52, 5) possible hands, with “a” being the rank of the three matching cards, and “b” and “c” being the ranks of the other two cards:

There are 13 ways to choose “a”. Of these, there are C(4, 3) ways to choose their suits.

Then, there are C(12, 2) to choose the ranks of “b” and “c”. Both cards’ suits may be chosen in 4 ways.

Then, the probability of being dealt three of a kind is the number of ways of being dealt three of a kind, divided by the total number of possible poker hands:

13 x C(4, 3) x C(12, 2) x 4 x 4 / C(52, 5)
= 54,912 / 2,598,960
~= .0211

Or, about 2.11%

Maroon 5 – Misery

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