How many 8-letter words with or without meaning, can be formed such that consonants and vowels occupy alternate positions?

Concept:

The number of ways of choosing m objects out of n different objects = nCm

The number of ways of arranging n objects = n!

Explanation:

Given word 'QUESTION' which has 8 different letters

{4 vowels (U,E,I,O) and 4 consonants(Q,S,T,N)}

If vowels occupy odd positions and consonants occupy even positions,

then 4 consonants are to be arranged in 4 positions and 4 vowels are to be arranged in 4 positions

As the number of ways of arranging 4 objects in 4 positions = 4! = 24

⇒ The number of ways arranging 4 vowels in 4 positions and 4 consonants in 4 positions = 24 × 24 = 576

Similarly, for the case when vowels occupy even positions and consonants occupy odd positions

So, the number of 8-letter words that can be formed such that consonants and vowels occupy alternate positions = 576 × 2 = 1152

∴ The correct answer is option (3).