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In a raffle with 100 tickets, 5 people buy 20 tickets each. If There are 3...

In a raffle with 100 tickets, 5 people buy 20 tickets each. If There are 3 winning tickets drawn at random find the probability that: a) one person gets all 3 winning tickets; b) there are 3 different winners; c) some person gets two winners and someone else gets just one.

Math   Statistics-And-Probability   
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Answer #1

a) The probability that one person gets all the winning tickets

b) There are lots of ways to solve this; here’s one. There are ways to choose which 3 people win— let’s name them A, B, C. The probability that A gets one winning ticket and 19 losing tickets is .

IF this happens, then the probability that B also gets one winning ticket and 19 losing tickets is   ,

because there are 2remaining winning tickets and 78 remaining losers. If both these happen, then the chance that C also gets one winning ticket and 19 losing tickets is , because 1 winning and 59 losing tickets remain;

thus the answer is

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