Question

The number of ways in which the letters of the word "VALEDICTORY" be arranged so that the vowels may never be separated is

• A. $7!4!$
• B. $8!4!$
• C. $7{!}^8{P}_4$
• D. $4!3!$

Answer 1

The correct option is B $8!4!$

The total number of vowels is four.

Making a pack of $4$, we get total $(11-4)+1$ objects

That is total of $8$ objects.

Now the number of ways of arranging $8$ objects is $8!$ ways.

There will be an internal arrangement of the vowels in $4!$ ...(4 vowels).

Hence the required permutation is

$8!(4!)$.