Chapter 12.6, Problem 5STP

For Exercises 1-7, choose the correct letter.

For a road trip, a friend is going to place 5 CDs into her CD player. She has 9 CDs to choose from. How many different selections of CDs can she make?

A. 126 B. 3024 C. 15,120 D. 362,880

To determine

Determine the value of the given statement.

Answer to Problem 5STP

A

Explanation of Solution

Given:

Given statement is :

For a road trip, a friend is going to place 5 CDs into her CD player. She has 9 CDs to choose from.How many different selections of CDs can she make.

Formula Used:

  $C{}_r=\frac{n!}{r!(n-r)!}$

Calculation:

Since we need to choose 5 CDs from 9 without replacement and order of CDs does not matter, so, the number of selections of CDs that she can make =

  $C{}_5=\frac{9!}{5!(9-5)!}=\frac{9!}{5!4!}=\frac{9\cdot 8\cdot 7\cdot 6}{4\cdot 3\cdot 2}=126$

So, the correct option is A.