# 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, 18 , 35 , 36 , None of These - Mathematics

MCQ

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

#### 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

Concept: Permutations
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Q 19 | Page 47

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