Q. 2 A5.0( 4 Votes )

# In how many ways can the letters of the word ‘STRANGE’ be arranged so thatthe vowels come together?

Given: the word is ‘STRANGE.’

To find: a number of arrangements in which vowels come together

Number of vowels in this word = 2(A, E)

Now, consider these two vowels as one entity(AE together as a single letter)

So, the total number of letters = 6(AE S T R N G)

Formula used:

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

Total number of arrangements

= the number of arrangements of 6 things taken all at a time

= P(6, 6)

{ 0! = 1}

= 6!

= 6 × 5 × 4 × 3 × 2 × 1

= 720

Two vowels which are together as a letter can be arranged in 2

Ways like EA or AE

Hence, total number of arrangements in which vowels come together = 2 × 720 = 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
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationFREE Class
Understand Permutations like never before60 mins
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