Question

Different words are being formed by arranging the letters of the word ARRANGE. All the words obtained are written in the form of a dictionary

Number of words in which at least one vowel between the two consonants is

• A. 341
• B. 342
• C. 36
• D. None of these

Answer 1

The correct option is C 36

First we write the consonants: $GNRR$

We arrange them in $\frac{4!}{2!}=12$ ways.

There are $3$ vowels and $3$ gaps between the consonants.

Now, we place $1$ vowel in each of the $3$ gaps.

Now, the vowels may be arranged in $\frac{3!}{2!}=3$ ways.
So, total = $12\times 3=36$

Hence, (C) is correct.