In how many different ways can the letters of the word "ACTIVE" be arranged so that the vowels occupy only odd positions?

Question: In how many different ways can the letters of the word "ACTIVE" be arranged so that the vowels occupy only odd positions?

Solution:
The word "ACTIVE" consists of the letters, Vowels are (A, I, E) and Consonants (C, T, V)

The number of ways to arrange the 3 vowels in the 3 odd positions is = 3!
= 6

The number of ways to arrange the 3 consonants in the 3 even positions is = 3! = 6

∴ The requried ways = (6 × 6)
= 36