Chapter 11.7, Problem 1C

To determine

The number of combinations of CD that can be bought.

Answer to Problem 1C

  $4\text{ combinations of CDs can be bought}\text{. }$

Explanation of Solution

Given information:

Consider the information provided in the question:

  $\text{There are }4\text{ different CDs to buy}\text{.Only 3 CDs can be afforded}\text{. }$

Formula used:

To find the number of combinations of $n$ objects taken $r$ at a time, divide the number of permutations of $n$ objects taken $r$ at a time by $r!$

  ${}_n{C}_r=\frac{{}_n{P}_r}{r!}$

Calculation:

As per the problem,

Consider $4\text{ different CDs to buy of which only 3 can be bought}\text{.}$

To calculate the number of combinations of CDs that can be bought, use formula

  ${}_n{C}_r=\frac{{}_n{P}_r}{r!}$

Substitute $4\text{ for }n\text{ and 3 for }r$

  ${}_4{C}_3=\frac{{}_4{P}_3}{3!}$

  $=\frac{4\cdot 3\cdot 2}{3\cdot 2\cdot 1}$ [Write ${}_4{P}_3$ and $3!$ as products]

  $=4$ [Divide out common factors and simplify]

Hence,

  $4\text{ combinations of CDs can be bought}\text{. }$