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Chapter 11: Problem 62

Fifty people purchase raffle tickets. Three winning tickets are selected at random. If each prize is \(\$ 500,\) in how many different ways can the prizes be awarded?

Short Answer

Expert verified
The three prizes can be awarded in 19600 different ways.

Step by step solution

01

Identify the knowns

In this exercise, the total number of people purchasing raffle tickets is given as fifty, and the number of prizes available to be awarded is three.
02

Identify the approach to solve

The concepts of combinations is useful here as we need to find out how many ways we can select 3 winners from 50 people, without considering the order of selection. This could be written as \(C(n,r) = n! / r!(n-r)!\), where n is the total number of options, r is the number of selections, and ! indicates factorial.
03

Carry out the calculation

Plug the values of n=50 (total people) and r=3 (total prizes) in the combination formula defined in previous step. The calculation should be \(C(50,3) = 50! / 3!(50-3)!\).

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