Question 1132012: A bridge hand is made up of 13 cards from a deck of 52. Find the probability that a hand chosen at random contains only hearts.
Found 2 solutions by math_helper, rothauserc:
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! P(first card is a heart) = 13/52
P(2nd card is also a heart) = 12/51
. . .
P(12th card is also a heart) = 2/41
P(13th card is also a heart) = 1/40
P(all 13 cards are hearts) = (13/52)(12/51). . .(2/41)(1/40)
( = 13! / P(52,13) )
= 
Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! There are (52C13) = 635,013,559,600, where 52C13 = 52!/(13! * (52-13)!)
:
possible hands, and only 4 of them (spades, hearts, diamonds, clubs) have a single 13-card suit
:
4/635,013,559,600 = 1/158,753,389,900
:
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That’s 1 out of every 158 billion+ hands
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