Quiz about Permutations and Combinations

Question 1

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?

Accepted Answer

Permutation - the order of the songs matters

Answer

Combination - the order of the songs does not matter

Question 2

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?

Accepted Answer

504

Answer

84

Answer

9!

Answer

3!

Question 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?

Is this a Permutation or a Combination?

Accepted Answer

Combination - the order does not matter

Answer

Permutation - the order matters

Question 4

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

Accepted Answer

20

Answer

6!

Answer

120

Answer

3!

Question 5

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?

Accepted Answer

Combination - the order does not matter

Answer

Permutation - the order matters

Question 6

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?

Is this a Permutation or a Combination?

Accepted Answer

Permutation - the order matters

Answer

Combination - the order does not matter

Question 7

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?

Accepted Answer

720

Answer

120

Answer

10!

Answer

3!

Question 8

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?

Accepted Answer

Permutation - the order matters

Answer

Combination - the order does not matter

Question 9

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?

Accepted Answer

Combination - order doesn't matter

Answer

Permutation - order matters

Question 10

The model of car you are thinking of purchasing is available in nine different colors, three different styles and two sizes of motor. How many ways can you order the car?

Is this a factorial problem or a counting principle problem?

Accepted Answer

Counting Principle - there are different categories to pick from

Answer

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

Question 11

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?

Accepted Answer

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

Answer

Counting Principle - there are different categories to pick from

Question 12

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

Accepted Answer

8!

Answer

6!

Answer

4!

Answer

8

Permutations and Combinations

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