Factorial, Permutation and Combination

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

You have DVD collection with 20 DVDs. You can only take five DVDs with you on vacation. How many different sets of five DVDs can you take?

• 15504

• 20!

• 5!

How many ways can you line up your eight trophies that you've won over the years on a shelf in your room? Is this a factorial problem or a counting principle problem?

• Factorial - there are a group of objects that need to be put in order

• Counting Principle - there are different categories to pick from

How many ways can you line up your eight trophies that you've won over the years on a shelf in your room?

• 6!

• 8!

• 4!

• 8

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!

A book club offers a choice of 8 books from a list of 40. In how many ways can a member make a collection?

Is this a Permutation or a Combination?

• Permutation - the order matters

• Combination - the order does not matter

A book club offers a choice of 8 books from a list of 40. In how many ways can a member make a collection?

• 40!

• 8!

• 76904685

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?

• 3!

• 2730

• 15!

You have DVD collection with 20 DVDs. You can only take five DVDs with you on vacation. How many different sets of five DVDs can you take?

Is this a Permutation or a Combination?

• Permutation - order matters

• Combination - order doesn't matter