Question

A department store is holding a drawing to give away free shopping sprees. There are 10 customers who have entered the drawing: 3 live in the town of Gaston, 5 live in Pike, and 2 live in Wells. Two winners will be selected at random. What is the probability that both winners live in Pike? Write your answer as a fraction in simplest form.

Answer 1

There are 10·9/2 = 45 ways to choose 2 winners from 10 entrants.

There are 5·4/2 = 10 ways to choose 2 winners from Pike.

The probability that both winners are from Pike is 10/45 = 2/9.

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There are n ways to choose the first winner from a pool of n. There are n-1 ways to choose the second one, hence n(n-1) ways to choose two from n when order matters. Since this counts the choices (1)(2) and (2)(1) as two different possibilities, we need to divide by 2 when order doesn't matter.