Question
Download Solution PDFHow many words can be formed the letters of the word 'DAUGHTER' so that the vowels always come together ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The number of ways to arrange n distinct things taken all at a time is given by: \({\;^n}{P_n} = n!\)
Calculation:
Given: 'DAUGHTER'
No. of distinct letters in the word 'DAUGHTER' = 8
Vowels in the word 'DAUGHTER' are A, E, U
No. of vowels in the word 'DAUGHTER' = 3
Consider the vowels as one group i.e (A, E, U), D, G, H, T, R then there are 6 letters which needs to be arranged.
As we know that, the number of ways to arrange n distinct things taken all at a time is given by: \({\;^n}{P_n} = n!\)
∴ No. of ways to arrange 6 letters = 6!
∵ There are 3 vowels in the group formed.
So, number of ways to arrange these vowels = 3!
∴ The required no. of words = 6! × 3! = 4320
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