Question
Download Solution PDFComprehension
How many 8-letter words with or without meaning, can be formed so that all consonants are together?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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).
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