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.
Solution:
(c) 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.
$\therefore$ 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 eitherĀ VCVCVC or CVCVCV.
$\therefore$ Total number of words $=18 \times 2=36$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.