Q. 2 C5.0( 3 Votes )

# In how many ways can the letters of the word ‘STRANGE’ be arranged so thatthe vowels occupy only the odd places?

Given: the word is ‘STRANGE.’

To find: number of arrangements so that the vowels occupy only odd positions

Number of vowels in word ‘STRANGE’ = 2(E, A)

Number of consonants = 5(S, T, R, N, G)

Let vowels be denoted by V

Odd positions are 1, 3, 5 or 7

So, fix the position by Vowels like this:

Now, arrange these 2 vowels at 4 odd places

Formula used:

Number of arrangements of n things taken r at a time = P(n, r)

Total number of arrangements of vowels

= the number of arrangements of 4 things taken 2 at a time

= P(4, 2)

= 4 × 3

= 12

The remaining 3 even places and 2 odd places can be occupied by 5 consonants

So, arrange these consonants at these places

Formula used:

Number of arrangements of n things taken all at a time = P(n, n)

Total number of arrangements of consonants

= the number of arrangements of 5 things taken all at a time

= P(5, 5)

0! = 1}

= 5!

= 5 × 4 × 3 × 2 × 1

= 120

Hence, the number of arrangements so that the vowels occupy only odd positions = 12 × 120 = 1440

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
Interactive Quiz on Combinations-0253 mins
Interactive Quiz on Combinations50 mins
Division and distribution of objects58 mins
Lecture on Combinations49 mins
Interactive Quiz on Division and distribution of objects17 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