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 all vowels occur together.

• A. $43200$
• B. $21600$
• C. $151200$
• D. None of these

Answer 1

Answer: (C)

$151200$

Taking all vowels as one, we have 7 elements to be arranged in $\frac{7!}{2!}$ ways (since there are 2 T's).

Now, the vowels can arrange among themselves in $\frac{6!}{2!3!}$ ways (since we have I 2 times and E 3 times).

Thus, total arrangements = $\frac{6!}{2!3!}\times \frac{7!}{2!}=60\times 2520=151200$

Hence, (c) is correct.