How many highcard poker hands are there A highcard poker han

How many high-card poker hands are there? A high-card poker hand is one which has no pairs and no flushes.

Solution

Event A - making pair

Event B-making flush both events are independant as you cannot make both in one game

now ways of not making pair= ~A= 13C5 * 4^5 you can select all different value/digit cards and you wont be able to make pair and each card having 4 possibilities of colour hence 4^5

A= total ways -~A

now ways of making flush=13C5 * 4 you should select all cards from same suit 13 C5 and 4 ways of making flush from each suit

and total ways of selecting 5 cards =52C5

P= 1-P(~A)+P(B)= 1+ (13C5(-4^5+4))/52C5

P= .49489

~P=.50511