Question

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

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

Answer 1

Answer: (D)

$\frac{{}^{11}{P}_5}{2}$

Vowels$=$EIEEI

Consonants$=$NGNRNG

For permuting consonants$={}^{11}{C}_6\times \frac{6!}{3!2!}$

and only $1$ choice for vowels (order same)

$\Rightarrow$ Total$=\frac{11!}{6!5!}\times \frac{6!}{3!2!}=\frac{11!}{5!\times 3\times 2\times 2}$

$=\frac{11!}{6!\times 2}=\frac{{}^{11}{P}_5}{2}$

$\Rightarrow \left(D\right)$.