Chapter 12.6, Problem 38PPE

To determine

To calculate: The number of different groups of 3 CDs selected from the 8 CDs.

Answer to Problem 38PPE

There are $56$ different groups.

Explanation of Solution

Given information:

The person received a gift of 3CDs from a music store. There are 8 CDs that is liked by a person.

Formula used:

A combination is a selection of objects without regard to order. The expression $C{}_r$ represents the number of combination of $n$ objects chosen $r$ at a time.

  $C{}_r=\frac{n!}{r!\left(n-r\right)!}$

For any positive integer $n$, the expression $n$ factorial is written as $n!$ and is the product of integers from n down to 1.

Calculation:

According to the question,

Total number of CDs liked by a person are 8.

Number of CDs received was 3.

Now,

  $\begin{array}{l}C{}_3=\frac{8!}{3!\left(8-3\right)!}\\ =\frac{8!}{3!5!}\\ =\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{5\times 4\times 3\times 2\times 1\times 3\times 2\times 1}\end{array}$

  $\begin{array}{l}=\frac{8\times 7\times 6}{3\times 2\times 1}\\ =4\times 7\times 2\\ =56\end{array}$

Hence, there are $56$ different groups of 3 CDs that person can select from the 8 CDs .