Chapter 0.5, Problem 10E

To determine

whether each situation involves a permutation or a combination and then to find the number of possibilities.

Answer to Problem 10E

The numbers of possibilities are 90720.

Explanation of Solution

Given information :

It is given that arrangement of letters in the word ‘ intercept’ .

In the given event, the order of the letters in line matter, therefore, it is a permutation.

The number of possibilities is given by,

  $\begin{array}{c}=\frac{9!}{2!2!}\\ =\frac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2}{2\times 1\times 2\times 1}\\ =90720possibilities\end{array}$

So, the numbers of possibilities are 90720.