Question

The number of permutations of the letters of the word $\text{CONSEQUENCE}$ in which all the three $\text{E's}$ arc together, is:

• A. $9!3!$
• B. $\frac{9!}{2!2!}$
• C. $\frac{9!}{2!2!3!}$
• D. $\frac{9!}{2!3!}$

Answer 1

The correct option is B

$\frac{9!}{2!2!}$

Explanation for the correct option(s)

Find the number of permutations of the letters

Consider the given word $\text{CONSEQUENCE}$

The number of letters in the word $\text{CONSEQUENCE}$ is $11$ letters.

The repeating letters are two $\text{C's}$, three $\text{E's}$, two $\text{N's}$, $\text{O, Q, S}$, and $\text{U}$ only one letters are there.

If all three $\text{E's}$ are together in out of $11$ letters, then remaining letters will be $8$.

Hence, the total letters will be $1+8=9$

The number of permutations of the letters can be expressed as $\frac{9!}{2!2!}$

Hence, option B is correct.