Question

Number of ways of permuting the letters of the word "ENGINEERING" so that the positions of the vowels is not changed is

• A. ${}^1{}^1{P}_5$
• B. $\frac{11!}{5!}$
• C. $\frac{11!}{2!5!}$
• D. $\frac{{}^1{}^1{P}_5}{2}$

Answer 1

The correct option is D $\frac{{}^1{}^1{P}_5}{2}$

Total number of ways of arranging $11$ things in a row is $11!$

However, we have considered here the permutations of the vowels also.

From these $11$ alphabets in the given word we have to keep the positions of the $5$ vowels fixed.

Also, we have $3$ N's and $2$ G's repeated.

$\therefore$ The required number of ways is $\frac{11!}{3!\times 2!\times 5!}=\frac{{}^{11}{P}_5}{2}$

Correct Option is D.