Question

If $M$ is the number of words that can be formed using letters of word "EXCELLENCE" and $N$ is the number of such words in which no two vowels are together, then $\frac{M}{N}$ is equal to

• A. $\frac{1}{4}$
• B. $\frac{5}{3}$
• C. $4$
• D. None of these

Answer 1

The correct option is B $\frac{5}{3}$

Total no. of words can be made $\frac{10!}{4!\times 2!\times 2!\times 1!\times 1!}$

$M=37800$

There are 4 E's i.e. vowels

let 2 E's be one unit $\therefore =\frac{9!}{1!\times 2!\times 2!\times 2!\times 1!\times 1!}$

$N=22680$

$\frac{M}{N}=\frac{5}{3}$