**Solutions**

*Read and understand the question*. This question is looking for the total number of permutations, or orders, of 4 different objects taken 4 at a time.*Read and understand the question*. This question is looking for the total number of permutations, or orders, of 6 different trophies taken 6 at a time.*Read and understand the question*. This question is looking for the total number of permutations, or orders, of 7 different objects taken 3 at a time.

*Make a plan*. Multiply the number of choices for each placement of the objects. An object can be used only once.

*Carry out the plan*. There are 4 choices for the first object, 3 for the second, 2 for the third, and 1 for the fourth. The number of permutations is therefore 4 × 3 × 2 × 1 = 24.

*Check your answer*. One way to check this solution is to divide the total number of permutations by each of the factors that were multiplied to see if the result is 1: 24 ÷ 4 = 6, 6 ÷ 3 = 2, and 2 ÷ 2 = 1, so this solution is checking.

*Make a plan*. Multiply the number of choices for each placement of the objects. An object can be used only once.

*Carry out the plan*. There are 6 choices for the first object, 5 for the second, 4 for the third, 3 for the fourth, 2 for the fifth, and only 1 for the sixth.

The number of permutations is therefore 6× 5 × 4 × 3 × 2 × 1 = 720.

*Check your answer*. One way to check this solution is to divide the total number of permutations by each of the factors that were multiplied to see if the result is 1.

- 720 ÷ 6 = 120

- 120 ÷ 5 = 24

- 24 ÷ 4 = 6

- 6 ÷ 3 = 2

and

- 2 ÷ 2 = 1

so this solution is checking.

*Make a plan*. Multiply the number of choices for each placement of the objects until 3 factors are used. An object can be used only once.

*Carry out the plan*. There are 7 choices for the first object, 6 for the second, and 5 for the third. The number of permutations is therefore 7 × 6 × 5 = 210.

*Check your answer*. One way to check this solution is to divide the total number of permutations by each of the factors that were multiplied to see if the result is 1.

- 210 ÷ 7 = 30

- 30 ÷ 6 = 5

and

- 5 ÷ 5 = 1

so this solution is checking.

**Practice 3**

**Problems**

- How many ways can 2 books be selected out of a series of 4 books if the order is not important?
- Tyler and his family are going on a trip. He would like to select some movies to watch in the car while traveling. How many different combinations of movies are there if he selects 4 movies to watch out of a total of 8?
- There are 6 students in a club. For a certain activity, 4 of the students need to form a separate group. How many ways can this group of 4 students be formed?

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