In the game of Paigow Poker a standard 52 card deck is used

In the game of Paigow Poker, a standard 52 card deck is used. If you are dealt 7 cards, what\'s the probability that you have 7 cards in a row and they all have the same suit? (called a straight flush) P.S. i got 0.00513% but want to be sure. Show all steps please

Solution

we hve to select 7 cards from 52 cards

N(s) = 52C7

all 7 cards of same suit

we have 4 suits where 13 cards are present in each suit

we have to select 7 cards from 13 cards of suit

we have 13C7 combinations from 1 suit

As there are 4 suits we have 4*13C7 ways

P(A) = n(A)/n(s) = 4*13C7/52C7 = 0.00513%