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Question

How many arrangements can be made out of the letters of the word draught, the vowels never being separated?

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Solution

The vowels are never being separated.
So, vowels a & u are taken together and considered as one letter.
So, there are 6 letters in the word draught
The number of ways in which it can be arranged are given by =6!=720.
But the internal arrangement can be done of a and u in 2 ways.
Hence the total arrangements are 720×2=1440.

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