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Question

How many words can be formed from the letters of the word 'DAUGHTER' so that the vowels always come together?

A
720
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B
2160
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C
4320
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D
None of these
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Solution

The correct option is C 4320
Take all the vowels A U E together and take them as one letter.
Then, the letters to be arranged are D, G, H, T, R, (A U E).
These 6 letters can be arranged in 6 places in 6! ways.
Now, 3 letters A, U, E among themselves can be arranged in 3!=6 ways.
required number of words =(6!)×6=(6×5×4×3×2×1×6)=4320.

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