Question

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

lf vowels & consonants occupy their original places, then the number of permutations is

• A. $\frac{6!}{2!}\times \frac{6!}{2!}$
• B. $\frac{6!}{3!}\times \frac{6!}{2!}$
• C. $\frac{6!\times 6!}{3!2!2!}$
• D. None of these

Answer 1

The correct option is C $\frac{6!\times 6!}{3!2!2!}$

We have:
I N T E R M E D I A T E
v c c v c c v c v v c v
The vowels may be arranged in their positions in $\frac{6!}{2!3!}$ ways (since we have I 2 times and E 3 times)
The consonants many be arranged in their positions in $\frac{6!}{2!}$ ways (since we have T 2 times)
Thus, total arrangements = $\frac{6!6!}{2!3!2!}$
Hence, (c) is correct.