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