A flush in 5 card stud poker is obtained if all 5 cards are

A flush in 5 card stud poker is obtained if all 5 cards are of the same suit, i.e., either 5 hearts, 5 diamonds, 5 spades, or 5 clubs. If you are dealt 5 cards, what is the probability of obtaining all hearts?

Solution

There are 13 hearts and total of 52 cards.

The, probability of obtaining all the 5 cards as hearts is:

P ( 5 hearts) = ¹³C₅ / ⁵²C₅ = 33 / 66640

= 4.95198 * 10^-4

Hope this helps.