A 5card poker hand is dealt from a well shuffled regular 52c

A 5-card poker hand is dealt from a well shuffled regular 52-card playing card deck. Find the probability that the hand is a Royal flush(10, J, Q, K, A all of the same suit).

Solution

The best hand (because of the low probability that it will occur) is the royal flush, which consists of 10, J, Q, K, A of the same suit. There are only 4 ways of getting such a hand (because there are 4 suits), so the probability of being dealt a royal flush is

4 / 52C5

= 4 / (52!/(5!*47!))

=0.000 001 539 Answer