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

• A. 18
• B. 35
• C. 36
• D. None of these

Answer 1

The correct option is C

36

The word APURBA is a 6 letter word consisting of 3 vowels that can be arranged in 3 alternate places, in 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 = 3!2! $\times$ 3! = 18

But this whole arrangement can be set-up in total two ways, i.e. either VCVCVC or CVCVCV.

$\therefore$ Total number of words = 18 $\times$ 2 = 36