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### Raffle Tickets

```
Date: 08/20/97 at 07:39:49
From: mostyn
Subject: Probability

What is the best way to do this:

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.

I figured it out using a tree diagram, and multiplying probabilities
of the branches, but is there a better way?
```

```
Date: 08/26/97 at 13:31:25
From: Doctor Rob
Subject: Re: Probability

Let C(a,b) = a!/(b!*(a-b)!).

(a) C(3,1)*C(97,4)/C(100,5)  is the probability of choosing
one out of the three winning tickets and choosing four
out of the 97 losing tickets as a favorable result of
choosing five out of the 100 tickets sold.

(b) This probability is 1 - C(3,0)*C(97,5)/C(100,5), since
the last term is the probability of choosing zero out of
the three winning tickets and five out of the 97 losing
tickets.

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Probability

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