Class 11

Math

Algebra

Permutations and Combinations

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

- $7!4!$
- $8!4!$
- $7!_{8}P_{4}$
- $4!3!$

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

$8!(4!)$.