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# A man buys 5 tickets in a raffle in which 100 tickets are

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A man buys 5 tickets in a raffle in which 100 tickets are [#permalink]  04 Jan 2005, 12:01
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A man buys 5 tickets in a raffle in which 100 tickets are sold. If
there are three prizes in the raffle, find the probability that the
man:

(a) wins exactly one prize;
(b) wins at least one prize.
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A. 3 prizes of which he wants 1 can be done in (3c1) ways. 97 non prizes of which he wants 4 can be done in (97c4) ways. Total ways to draw 5 out of 100=(100c5). So the answer is (3c1)*(97c4)/(100c5)

B. Same reasoning as above but also for 2 and 3 prizes so [(3c1)*(97c4) + (3c2)*(97c3)+(3c3)*(97c2)]/(100c5)
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