Permutations and Combinations

The ski club has 10 members and is choosing three officers for the season. How many ways can they pick a captain, co-captain and secretary?

• 720

• 120

• 10!

• 3!

An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

• 6!

• 120

• 20

• 3!

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

• 15
• 40
• 80
• 10

How many total outfit options are represented?

• 12
• 22
• 3

Sarah plays softball over the summer.  If there are 10 players on the team, how many ways can the coach make a batting order that includes all players?

• 1
• 3628800
• 100
• 1814400

In the orchestra, there are eight violinists in the front row. How many different ways can they be seated?

• 40320
• 1
• 64
• 8

Eva has eight glasses of water.  In how many different orders can the glasses of water be arranged?

• 8
• 64
• 8!
• 56

Robin has five different pairs of shoes that match with 6 different pairs of socks.  How many shoes-and-socks combinations can she make if she selects one pair of shoes and one pair of socks?

• 1
• 30
• 5!
• 6!

Rylan’s basketball team has 11 players. How many ways can his coach choose five starting players?

• 462
• 55440
• 55
• 1000

There are 14 candy bars for sale. How many ways can Andy choose five of them?

• 240240
• 2002
• 87178291200
• 70