Question

Total number of words that can be formed using all letters of the word $FAILURE$ which neither begin with$F$ nor end with $E$ is equal to

• A. $3720$
• B. $5040$
• C. $3600$
• D. $3480$

Answer 1

The correct option is A

$3720$

Explanation for the correct option:

Find the required number of permutations:

In the question, the word FAILURE is given.

So, the total number of permutations of the given words are $7!$.

And the number of words that starts with $F$ and ends with $E$ are $5!$.

And the number of words that starts with $F$ or ends with $E$ are $2(6!)$.

So, the total number of permutations that neither begin with $F$ nor end with $E$ is given by $7!+5!-2(6!)=3720$.

Therefore, the total number of words that can be formed using all letters of the word FAILURE which neither begin with $F$ nor end with $E$ is equal to $3720$.

Hence, option (A) is the correct answer.