Chapter 10.5, Problem 3E

(a)

To determine

To calculate:

All of the letters in the given word

  $AT$

Answer to Problem 3E

All of the letters in the given word $AT$ is $2$ .

Explanation of Solution

Given information:

  $AT$

Calculation:

The formula for permutation for $n$ objects is:

  $P{}_n=n!$

Where,

  $n=2$

There are total two words in this letter $AT$ .

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

  $P{}_2=2!=2$

Hence, all of the letters in the given word $AT$ is $2$ .

(b)

To determine

To calculate:

Two of the letter in this word

  $AT$

Answer to Problem 3E

The two of the letters in the given word $AT$ is $2$ .

Explanation of Solution

Given information:

  $AT$

Calculation:

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

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

Where,

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

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

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

Hence, two of the letters in the given word $AT$ is $2$ .