what is the probability of three of a kind out of a standard

what is the probability of three of a kind out of a standard deck of 52 cards?

Solution

There are 52C3 ways to choose any 3 cards.

There are 4C3 = 4 three-of-a-kinds in each rank, and there are 13 ranks. Thus, there are 4*13 = 52 three of a kinds.

Thus,

P(three of a kind) = 52 / 52C3 = 0.002352941 [answer]