Question

There are 5 people in a raffle drawing. Two 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 combination, and then find the number of ways to choose the winners.

A.
Permutation; number of ways = 20
B.
Combination; number of ways = 20
C.
Permutation; number of ways = 10
D.
Combination; number of ways = 10

Answer 1

D.

Combination; number of ways = 10

Explanation:

Permutation is when order matters

Combinations is when order doesn't matter.

Since there are two identical gift cards, it doesn't matter who gets the first gift card and who gets the second gift card, so this is a combination

There are 5 people choose 2

n!

--------

r!(n − r)!

where n is the number of items and r is how many we choose

5! 5*4*3*2*1

-------- = ------------------ = 10

2! (5-2)! 2*1 ( 3*2*1)

D.

Combination; number of ways = 10