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. $Noneofthese$

Answer 1

The correct option is A

$16800$

Finding arrangement.

Given words is ‘INDEPENDENCE’ total number of letter is $12$out which $5$ are vowel (I, E, E, E, E) & $7$ are constant ‘N, D, P, N, D, N & C’

Keeping all vowel together then total number words form this words is $(7+1=8places)$ $=\frac{8!}{3!\times 2!}=3360$ as ‘N & D’ is repeated thrice and twice.

The group of 5 vowels can be arranged in $\frac{5!}{4!}=5$ as ‘E’ repeated four times

Therefore, total arrangement is given by $3360\times 5=16800$

Hence, correct answer is $\mathbf{\left(}\mathit{A}\mathbf{\right)}$.