In five-card poker, a straight consists of five cards with adjacent denominations (e.g., 9 of clubs, 10 of hearts, jack of hearts, queen of spades, and king of clubs). Assuming that aces can be high or low, if you are dealt a five-card hand, what is the probability that it will be a straight with high card 10? What is the probability that it will be a straight? What is the probability that it will be a straight flush (all cards in the same suit)?

Solution: Step 1: It is given that a straight is consists of five cards with adjacent denominations (e.g., 9 of clubs, 10 of hearts, jack of hearts, queen of spades, and king of clubs). And we dealt a five- card hand. Here aces can be high or low. Step 2: 1) We have to find the probability that it will be a straight with high card 10. 52 The number of ways to select 5 cards from 52 cards is = C 5 = ,598,960. A straight with high of 10 means the other 4 cards must be from different denominations which are less than 10. So we can select the 5 cards with denominations 6,7,8,9,10 . since there are 4 cards of each number in a set of cards. Hence the possible number of ways to select the the 5 cards are 5 = 4*4*4*4*4= 4 So the probability of a straight with high card 10 will be 5 p( straight with high card 10) = 4 2598960