1 pt A 5card poker hand is dealt from a well shuffled regula

(1 pt) A 5-card poker hand is dealt from a well shuffled regular 52-card playing card deck. Find the probability that the hand is a Four of a kind (4 cards of the same face value).

Solution

There are 52C5 ways to choose any 5 cards.

There are 13 ways to choose a four of a kind, one for each rank, and 48 ways to choose the 5th card.

Thus,

P(four of a kind) = (13*48)/(52C5) = 0.000240096 [ANSWER]