Combinations and Permutations

Find the number of possibilities:
A group of 25 people are going to run a race.  The top 8 finishers advance to finals.

• 625
• 4.36 X 10¹⁰
• 1,081,575

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

• 15
• 40
• 80
• 10

Two number cubes are rolled, then a spinner with 4 different colors on it is spun twice, then two coins are flipped. How many total possible outcomes are there?

• 4096

• 24

• 46,656

• 2,304

At Papa John's you are deciding on what you want for dinner. The pizza offers 8 different meats, 4 different cheeses, 3 different crust types and 2 different sauces. How many different pizzas do you have to choose from?

• 32
• 192
• 40,320
• 51,200

A DJ has to choose three songs for the last few minutes of his evening show. If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose and arrange to play three of those nine songs?

Is this a Permutation or Combination?

• Permutation - the order of the songs matters

• Combination - the order of the songs does not matter

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

Is this a Permutation or a Combination?

• Permutation - the order matters

• Combination - the order does not matter

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!

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!

There are 15 racers running a race. There are medals for the first three racers to cross the finish line. How many ways are there to award medals to the first three racers?

Is this a Permutation or a Combination?

• Permutation - the order matters

• Combination - the order does not matter

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

• 462
• 55440
• 55
• 1000