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

A royal flush is ace, queen, king , jack and 10 of the same suit. If 5 car hand is ordered from highest to lowest, the first card will be an ace. There are 4 possible suits for ace.

Thus, the number of royal flushes are: 4C1=4

The number of possible 5 card hand is 52C5=2598960

Divide it by number of possible hands to get

P(royal flush)=4/2598960=