SOLUTION: Five cards are down in succession from a deck of 52 playing cards and after each card is drawn it is not replaced in the deck. What is the probability that all five cards are of th

Question 628467: Five cards are down in succession from a deck of 52 playing cards and after each card is drawn it is not replaced in the deck. What is the probability that all five cards are of the same suit?

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Five cards are down in succession from a deck of 52 playing cards and after each card is drawn it is not replaced in the deck. What is the probability that all five cards are of the same suit?
first card: 13/52 = 1/4
second card: 12/51 = 4/17
third card: 11/50
fourth card: 10/49
fifth card: 9/48
probability:
1/4 * 4/17 * 11/50 * 10/49 * 9/48
= 1/4 * 1/17 * 11/50 * 10/49 * 9/12
= 1/4 * 1/17 * 11/50 * 5/49 * 9/6
= 1/4 * 1/17 * 11/10 * 1/49 * 9/6
= 0.002 = .2%
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