Chapter 10.5, Problem 4E

(a)

To determine

To calculate:

All of the letters in the given word

  $TRY$

Answer to Problem 4E

All of the letters in the given word $TRY$ is $6$ .

Explanation of Solution

Given information:

  $TRY$

Calculation:

The formula for permutation for $n$ objects is:

  $P{}_n=n!$

Where,

  $n=3$

There are total three words in this letter $TRY$ .

The number of the permutations to arrange all of letters is as:

  $\begin{array}{l}P{}_3=3!\\ P{}_3=3\times 2\times 1\\ P{}_3=6\end{array}$

Hence, all of the letters in the given word $TRY$ is $6$ .

(b)

To determine

To calculate:

Two of the letter in this word

  $TRY$

Answer to Problem 4E

The two of the letters in the given word $TRY$ is $6$ .

Explanation of Solution

Given information:

  $TRY$

Calculation:

The formula for permutation for $n$ objects taken $r$ at the time is as:

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

Where,

  $\begin{array}{l}n=3\\ r=2\end{array}$

The number of the permutations to arrange two of letters is as:

  $\begin{array}{l}P{}_2=\frac{3!}{\left(3-2\right)!}\\ P{}_2=3!=3\times 2\times 1\\ P{}_2=6\end{array}$

Hence, two of the letters in the given word $TRY$ is $6$ .