Chapter 12.5, Problem 49E

a.

To determine

Find the different arrangement of letters in this word is possible.

Answer to Problem 49E

  $720$

Explanation of Solution

Given information:

Consider the word “SILENT”

Calculation:

The word “SILENT” has six letters.

There are $6$ ways to choose the first letter.

There are $5$ ways to choose the second letter

There are $4$ ways to choose the third letter

There are $3$ ways to choose the fourth letter

There are $2$ ways to choose the fifth letter

There are $1$ ways to choose the sixth letter

The possible different arrangements are,

  $\begin{array}{l}6!\\ 6\times 5\times 4\times 3\times 2\times 1=720\end{array}$

Hence, the different arrangement of letters is $720$ .

b.

To determine

Find the different arrangement still remains.

Answer to Problem 49E

  $120$

Explanation of Solution

Given information:

Consider the word “SILENT” if anagram of this word starts with “L”.

Calculation:

Now only five letters be considered,

There are $5$ ways to choose the second letter

There are $4$ ways to choose the third letter

There are $3$ ways to choose the fourth letter

There are $2$ ways to choose the fifth letter

There are $1$ ways to choose the sixth letter

The possible different arrangements are,

  $\begin{array}{l}5!\\ 5\times 4\times 3\times 2\times 1=120\end{array}$

Hence, the different arrangement of letters is $120$ .

c.

To determine

Find the different arrangement still remains also write the suggested anagram.

Answer to Problem 49E

  $24$ ,“LISTEN”.

Explanation of Solution

Given information:

Consider the word “SILENT” the last letter in the anagram is “N”

Calculation:

Now only four letters be considered,

There are $4$ ways to choose the third letter

There are $3$ ways to choose the fourth letter

There are $2$ ways to choose the fifth letter

The possible different arrangements are,

  $4\times 3\times 2=24$

To write the suggested anagram containing first letter “L” and last letter “N” the only word that make sense is “LISTEN”

Hence, the different arrangement of letters $24$ and anagram is “LISTEN”.