Probability of being dealt a straight flush

Question

A standard deck of cards is completely shuffled and randomized. It is then dealt into four separate piles of 13 cards each. What is the chance that one of these piles will have a straight flush?

Answer 1

A straight flush is 5 cards of any of 4 suits in sequential order. The ace can be considered high or low. There are 52 cards in a deck. The number of possibilities of drawing 5 cards from the deck are C_52,5 = 52*51*50*49*48/5! = 2,598,960.  There are 10 possible ways for each suit to get a sequence of 5 consecutive cards. For example, AKQJ10, 5432A, 98765, etc. So with 10 ways and 4 suits this is 4* 10 = 40.

 

The probability of a straight flush = 40/2,598,960 = 0.000015. This assumes you are talking about a 5 card flush, not each hand of 13 cards all having the same suit.