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In another lesson, we will consider the number of permutations of

* Example*

Suppose we want to take a picture of three boys, Allen, Bryan and Carlos. In how many ways can the boys be arranged?

*Solution: *

They can be arranged in any of several ways.

Allen Bryan Carlos

Allen Carlos Bryan

Bryan Allen Carlos

Bryan Carlos Allen

Carlos Allen Bryan

Carlos Bryan Allen

There are 3 choices for the first boy, 2 choices for the second and 1 choice for the third, so the total number of permutations is 3 x 2 x 1 = 6. The 3 boys can be arranged in 6 ways.

In this example, the symbol P(3, 3) represents the number of permutations of 3 things taken 3 at a time.

P(3, 3) = 3 × 2 × 1 = 6

*Example: *

In how many ways can 6 people be seated in a row of 6 chairs?

*Solution: *

We can use the permutation formula P(6, 6) which is 6 things taken 6 at a time.

P(6, 6) = 6 × 5 × 4 × 3 × 2 × 1

Six people can be seated in 720 ways.

*Example: *

In how many ways can seven different books be arranged on the shelf?

*Solution: *

We can use the permutation formula P(7, 7) which is 6 things taken 6 at a time.

P(7, 7) = 7 × 6 × 5 × 4 × 3 × 2 × 1

The books can be arranged in 5,040 ways.

The following video gives another example of the permutation problem.You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.