Question

In how many ways can the letters in the word ATONEMENT be arranged?

Answer 1

Given:

The word is ATONEMENT.

The number of letters in this word are 9 and unique letters are 6.

Arrangement of the letter is calculated as,

$\begin{gathered} n\text{ letters are arranged in n! ways} \\ Arrangement=9!\text{ } \end{gathered}$

But as the 3 letters are repeated 2 times.

So, the number of unique arrangements are,

$\text{Arrangement}=\frac{9!}{2!2!2!}=\frac{362880}{8}=45360$

Answer: Number of arrangements are 45360.