Math 213, Section B1, Quiz 5 (Solution); Friday, March 2, 2007
1.
A 3-card hand is chosen at random from a 52-card deck. Find the
probability that all three chosen cards are of the same suit.
Simplify your answer to the extent possible.
Solution.
For a fixed suit there are 13 cards in this suit and hence C(13,3)
possible 3-card hands with all three cards of that suit. Since there are
4 suits, there are 4 ·C(13,3) 3-card hands such that all three chosen
cards are of the same suit. There are C(52,3) 3-card hands possible
for a 52-card deck.
Hence the probability that all three chosen cards are of the same suit
is:
4·C(13,3)
C(52,3) =4·13 ·12 ·11
52 ·51 ·50 == 12 ·11
51 ·50 =6·11
51 ·25 =66
1275 = 0.051764.
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