Permutations vs. Combinations

Example

• For example, suppose we are arranging the letters A, B and C.

• In a permutation, the arrangement ABC and ACB are different.

• But, in a combination, the arrangements ABC and ACB are the same because the order is not important.

Multiple Choice

Permutation, combination, or neither?
Rob and Mary are planning trips to 9 countries this year.  There are 13 countries they would like to visit.  They are deciding which countries to skip.

• combination

• permutation

• neither

Dropdown

Determine whether the question would be a permutation or combination: Five students from 90 will be selected to count ballots for the Class President election. How many groups of 5 students could be selected to count ballots?

Select answer

Match

Decide whether you'd solve using a Permutation, Combination, or simply need a single factorial, then match the cards accordingly.

• Permutation

• Combination

• Factorial

A lock has a code of 3 numbers between 1 and 15. How many codes can be created if no numbers repeat

The principal would like to assemble a committee of 8 students from the 12-member student council.

Ribbons are being awarded for 1st through 5th place to the top 5 dogs in a dog show.

• A lock has a code of 3 numbers between 1 and 15. How many codes can be created if no numbers repeat

• The principal would like to assemble a committee of 8 students from the 12-member student council.

• Ribbons are being awarded for 1st through 5th place to the top 5 dogs in a dog show.

Multiple Choice

True or False: the order DOES matter in a permutation.

• True

• False

Drag and Drop

Determine whether the following scenarios are a permutation or a combination:
 

Placeholder

Drag these tiles and drop them in the correct blank above

Permutation

Combination

Multiple Choice

True or False: the order DOES matter in a combination.

• True

• False

Multiple Choice

Picking four players to play a pickup game of basketball with no positions.

• Permutation

• Combination

Multiple Choice

Choosing 3 toppings for your sundae out of a list of 15.

• Permutation

• Combination

• Neither

Multiple Choice

What does ₁₀P₅ mean?

• Permutations with 5 choices and 10 positions

• Permutations with 10 choices and 5 positions

• Permutations with 5 numbers and 10 operations

• Permutations with 5 hot dogs and 10 drinks

Multiple Choice

How many ways can you arrange 7 books on a shelf?

• 7

• 49

• 343

• 5,040

Multiple Choice

There are 18 people running in a cross country race. How many possible ways are there to place the runners in first, second, and third?

• 324

• 4,896

• 816

• 54

Multiple Choice

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

Math Response

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

Type answer here

Correct Answer: 40320

Deg^°

Rad

Multiple Choice

The ski club with ten members is to choose three officers for captain, co-captain and secretary.  How many ways can those offices be filled?

• 720
• 120
• 10!

Multiple Choice

How many 2-digit numbers can you make using the digits 1, 2, 3, & 4 without repeating the digits?

• 90
• 100
• 12
• 24

Multiple Choice

A disc jockey 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?

• 84
• 504
• 9!
• 3!

Multiple Choice

How many ways can you choose a manager and assistant from a 9-person task force?

• 81
• 18
• 72

Multiple Choice

Find the number of possibilities:
A team of 17 softball players needs to choose three players to refill the water cooler.

• 272

• 4080

• 680

Multiple Choice

How many ways can a stylist arrange 5 of 8 vases from left to right in a store display?

• 672
• 40
• 6720

Multiple Choice

Runners finishing top three in a race to qualify for the Olympics. The order they finish in is irrelevant as long as they are top three.

• Permutation

• Combination

Multiple Choice

Arranging letters to make a password.

• Permutation

• Combination

Fill in the Blanks

A club with 10 members is to choose four officers -- President, Vice-President, Treasurer, and Secretary. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?

Multiple Choice

Determine the number of 4-letter arrangements that can be made using the word RHOMBUS.

• 5040

• 35

• 28

• 840