A poker hand consisting of 5 cards is dealt from a standard

A poker hand, consisting of 5 cards, is dealt from a standard deck of 52 cards. Find the probability that the hand contains an ace, king, queen, jack, and 10 of the same suit (royal flush).

Solution

There are 52C5 = 2598960 ways to draw 5 cards.

Also, there are 4 such royal flushes, one of each suit.

Thus, the probability of a royal flush is

P(royal flush) = 4/2598960 = 0.00000153908 [ANSWER]