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,

The number of arrangements in which vowels & consonants occur alternatively are

• A. $43300$
• B. $43200$
• C. $21600$
• D. None of these

Answer 1

The correct option is B $43200$

There are 6 vowels and 6 consonants.

Thus, to occur alternately, the series may start with a consonant OR a vowel i.e. there are $2$ cases.

The vowels may be arranged in $\frac{6!}{2!3!}$ ways (since we have I 2 times and E 3 times)

The consonants many be arranged in $\frac{6!}{2!}$ ways (since we have T 2 times)

Thus, total arrangements $=\frac{6!6!}{2!3!2!}\times 2=43200$
Hence, (B) is correct.