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

combination; number of ways = 10

Answer 2

• 10

Step-by-step 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=(m!)/(n!(m-n)!)\\ \\_3C_(5)=(5!)/(3!(5-3)!)=((5)(4))/((2)(1))=10`