Q. 44.3( 3 Votes )

# How many words can be formed out of the letters of the word, ‘ORIENTAL,’ so that the vowels always occupy the odd places?

Given: the word is ‘ORIENTAL.’

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

Number of vowels in the word ‘ORIENTAL’ = 4(O, I, E, A)

Number of consonants in given word = 4(R, N, T, L)

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 4 vowels at 4 places

Formula used:

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

Total number of arrangements of vowels

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

= P(4, 4)

{ 0! = 1}

= 4!

= 4 × 3 × 2 × 1

= 24

The remaining 4 even places can be occupied by 4 consonants

So, arrange 4 consonants at remaining 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 4 things taken all at a time

= P(4, 4)

{ 0! = 1}

= 4!

= 4 × 3 × 2 × 1

= 24

Hence, the number of arrangements so that the vowels occupy only odd positions = 24 × 24 = 576

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