Q. 2 A5.0( 4 Votes )

In how many ways can the letters of the word ‘STRANGE’ be arranged so that

the vowels come together?

Answer :

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


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