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?

Combination - order doesn't 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?

5 20 = 0.25 \frac{5}{20}=0.25 2 0 5 = 0 . 2 5

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?

Counting Principle - there are different categories to pick from

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

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?

9 ! 3 ! = 9 ⋅ 8 ⋅ 7 ⋅ 6 ⋅ 5 ⋅ 4 = 60480 \frac{9!}{3!}=9\cdot8\cdot7\cdot6\cdot5\cdot4=60480 3 ! 9 ! = 9 ⋅ 8 ⋅ 7 ⋅ 6 ⋅ 5 ⋅ 4 = 6 0 4 8 0

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

Permutations and Combinations

Authored by Ray Tartaglia

Mathematics

9th - 11th Grade

CCSS covered

Used 454+ times

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16 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

Tags

CCSS.HSS.CP.B.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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?

504

Tags

CCSS.HSS.CP.B.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

Tags

CCSS.HSS.CP.B.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

120

Tags

CCSS.HSS.CP.B.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

Tags

CCSS.HSS.CP.B.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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!

$\frac{8}{40}=0.2$

76904685

Tags

CCSS.HSS.CP.B.9

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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?

Permutation - the order matters

Combination - the order does not matter

Tags

CCSS.HSS.CP.B.9

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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?

$\frac{3}{15}=0.2$

2730

15!

Tags

CCSS.HSS.CP.B.9

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Permutations and Combinations

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?

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?

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?

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

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?

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

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?

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?

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?

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?

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Discover more resources for Mathematics

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?

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?

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?

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?

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?