Problem 62
Question
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?
Step-by-Step Solution
Verified Answer
The three prizes can be awarded in 19600 different ways.
1Step 1: 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.
2Step 2: 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.
3Step 3: 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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