Question

How many words can be made out from the letters of the word $INDEPENDENCE$, in which vowels always come together?

• A. $16800$
• B. $16630$
• C. $1663200$
• D. None of these

Answer 1

The correct option is A $16800$

There are $12$ letters in the word independence with $5$ vowel and $7$ consonants. Now, bunch up all $5$ vowel together as one letter so as to assume a word with $3$ letters which can be arranged in $\frac{3!}{3!2!}=3360$ ways

And the bunch of $5$ vowels can be arranged among themselves in $\frac{5!}{4!}=5$ ways. Hence, total arrangements of the letters with vowels always coming together is $5\times 3360=16800$.