Exercise 38 Page 705

We want to find out how many ways there are to assign three different roles in a play to 3 out of 10 students. Note that, in this case, the order is important. Therefore, each possible arrangement is a permutation. To calculate the answer, we will use the formula for permutations of n objects taken r at a time. _n P_r = n!/(n-r)! In our exercise, n=10 and r=3. Let's substitute 10 for n and 3 for r in the above formula.

_n P_r = n!/(n-r)!

SubstituteII

n= 10, r= 3

_(10) P_3 = 10!/( 10- 3)!

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Simplify

SubTerm

Subtract term

_(10) P_3 = 10!/7!

Write as a product

_(10) P_3 = 10* 9* 8* 7!/7!

ReduceFrac

a/b=.a /7!./.b /7!.

_(10) P_3 = 10* 9* 8/1

DivByOne

a/1=a

_(10) P_3 = 10* 9 * 8

Multiply

Multiply

_(10) P_3 = 720

There are 720 permutations.