Calculate the probability of being dealt the following poker

Calculate the probability of being dealt the following poker hand. (Recall that a poker player is dealt 5 cards at random from a standard deck of 52.) Express your answer as a decimal rounded to four decimal places.

Solution

(13 ranks, choose 2)*(4 from each rank, choose 2)
*(remaining 44 cards, choose 1) /(52 total, choose any 5)

= 13c2*(4c2)^2 *44 / 52c5 = 0.0475 <------