Q. 19

# Mark the correct alternative in the following:The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate isA. 18B. 35C. 36D. none of these

We have, 6 objects {A}, {P}, {U}, {R}, {B}, {A} and there are 2 A's, so, there are 3 vowels (2 {A}’s and 1 {U}) and 3 consonants ({P}, {R}, {B}).

The word arrangement where, vowels and consonants are alternate is shown below:

Arrangement-1:

Arrangement-2:

The vowel positions can be filled in ways, and the consonant positions can be filled in 3! ways.

As, the operations are dependent so, the number of ways to fill the 6 positions

So, 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

[as, we have 2 possible arrangements]

= 36.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Circular permutations61 mins
Challenging Quiz on P&C | Test Yourself55 mins
Permutations & Combinations | Analyze your learningFREE Class
Understand Permutations like never before60 mins
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationFREE Class
Lecture on Combinations49 mins
Interactive Quiz on Division and distribution of objects17 mins
Interactive Quiz on Combinations50 mins
Division and distribution of objects58 mins
Interactive Quiz on Combinations-0253 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses