Chapter 13.9, Problem 1BGP

To determine

The number of ways to place the four fruits of ten different fruits is to be described.

Answer to Problem 1BGP

The number of ways to place the four fruits of ten different fruits is $5040$ .

Explanation of Solution

Given:

  $\begin{array}{l}n=10\\ r=4\end{array}$

Concept Used:

The formula for combination is given by the following expression:

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

Calculation:

The number of ways to arrange four fruits is calculated by using the permutation and combination:

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

Put the given data in the above formula:

  $\begin{array}{l}C{}_4=\frac{n!}{\left(n-r\right)!}\\ C{}_4=\frac{10!}{\left(10-4\right)!}\\ C{}_4=\frac{10!}{6!}\\ C{}_4=10\times 9\times 8\times 7\\ C{}_4=5040\end{array}$

Conclusion:

Hence, the number of ways to arrange four fruits is $C{}_4=5040$