Question

There are 5 people in a raffle drawing. Three raffle winners each win gift cards. Each gift card is the same. How many ways are there to choose the winners? Decide if the situation involves a permutation or a combination, and then find the number of ways to choose the winners

Answer 1

Answer:

• 10

Explanation:

Call the wiiners of the gift cards W₁, W₂, and W₃.

Since each gift card is the same, any permutation of those three winners,  W₁, W₂, and W₃ are equivalent. This is what tells that the order of the winners does not matter and that the situation involves a combination instead of a permutation.

Then, you have to calculate the combination of 3 winners, selected from a group of 5 people; that is:

$_nC_m=\frac{m!}{n!(m-n)!}\\ \\_3C_{5}=\frac{5!}{3!(5-3)!}=\frac{(5)(4)}{(2)(1)}=10$