8th math Combinations and Permutations

Determine whether the question would be a permutation or combination, then answer the question.

You have selected 8 books this summer and want to read 6 of them, one at a time. In how many ways can you read the books (the books are not in a series).

Give you answer in symbolic form and as a number.

Determine permutation or combination, then answer the question. You are ordering a 2-topping pizza and can select the toppings from eight options. In how many different ways are there to order the pizza?

Give you answer in symbolic form and as a number.

Determine permutation or combination, then answer the question.

For your research paper, you find seven articles related to your topic. In how many ways can you select 5 articles to read?

Give you answer in symbolic form and as a number..

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! = 9*8*7*6*5*4*3**1

• 15

• $\frac{9!}{3!}=9\cdot8\cdot7\cdot6\cdot5\cdot4=60480$

• 54 = 9*3*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? Give you answer in symbolic form and as a number.

• 84

• 504

• 9!

• 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? Give you answer in symbolic form and as a number.

• 6!

• 120

• 20

• 3!

Determine whether the question would be a permutation or combination: In how many ways can the nine starting players on a baseball team be strategically placed on the lineup? Also give the symbolic form.

• Permutation

• Combination

• Neither

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? Give you answer in symbolic form and as a number.

• 720

• 120

• 10!

• 3!

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

• 6!

• 8!

• 4!

• 8

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