How many 8-letter words with or without meaning, can be formed so that all consonants are together?

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 all consonants are together consider them as one string, which can be rearranged internally in 4! ways 

⇒ Number of ways of rearranging 4 consonants = 24

Now for forming a word, we have to arrange 4 vowels and one string of consonants 

The number of ways of arranging 5 objects = 5! = 120

So, the total number of words formed = 120 × 24 = 2880

∴ The correct answer is option (2).