Discussion

Question:

How many words can be formed using all the letters of the word such that no two vowels are adjacent to each other?

Explanation:

Vowels here are: A, A, I, I, I, O i.e., 6 vowels.

Let us first arrange the 7 consonants.

∴ Number of ways of arranging these letters = $\frac{7!}{2!\times 2!}$.

Now, we have 8 spaces created to put these six vowels.

We can select any 6 of these in ⁸C₆ = 28 ways and arrange these 6 vowels in $\frac{6!}{2!\times 3!}$ ways.

∴ Total number of words that can be formed such that no two vowels are adjacent to each other = $\frac{7!}{2!\times 2!}$ × ⁸C₆ × $\frac{6!}{2!\times 3!}$ = 

Hence, option (d).

» Your doubt will be displayed only after approval.