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Question
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
Options
18
35
36
none of these
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Solution
36
The word APURBA is a 6 letter word consisting of 3 vowels that can be arranged in 3 alternate places, in\[\frac{3!}{2!}\]ways.
The remaining 3 consonants can be arranged in the remaining 3 places in 3! ways.
∴ Total number of words that can be formed =\[\frac{3!}{2!} \times 3!\] = 18
But this whole arrangement can be set-up in total two ways, i.e either VCVCVC or CVCVCV.
∴ Total number of words = 18 x 2 = 36
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