MathDB

Ryan Murphy is playing poker. He is dealt a hand of

5

cards. Given that the probability that he has a straight hand (the ranks are all consecutive; e.g.

3,4,5,6,7

9,10,J,Q,K

) or

3

of a kind (at least

3

cards of the same rank; e.g.

5, 5, 5, 7, 7

5, 5, 5, 7,K

) is

m/n

, where

m

and

n

are relatively prime positive integers, find

m +n

.
Proposed by Aditya Rao

Problem Statement