EXAMPLE 3 Evaluating a Permutation

Poetry

Two students are chosen from a group of 6 to read the first and second poems at the school’s poetry reading. To find how many different ways the students can be chosen, find 6P2.

6P2– == 6!

(6 2)!6!4!

Use permutation formula.

= 6 5 4 3 2 14 3 2 1

Divide out common factors.

= 30 Multiply.

ANSWER

The students can be chosen in 30 ways.

GUIDED PRACTICE for Example 3

Find the number of permutations.

6. 5P3 = 60

7. 6P6 = 720

GUIDED PRACTICE for Example 3

8. 8P7 = 40, 320

9. 100P2 = 9, 900

GUIDED PRACTICE for Example 3

10. What If?

Suppose 3 students are chosen from a group of 8 to read in Example 3. In how many different ways can the students be chosen?

To find how many different ways can the students be chosen, find . 8P3

= 3368P3