Latest AIEEE Aptitude Question SOLUTION: How many words can be formed from the letters of the word ‘DIRECTOR’ So that the vowels are always together?

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(#M40009692) AIEEE question Keep an EYE

How many words can be formed from the letters of the word ‘DIRECTOR’
So that the vowels are always together?

Asked In AIEEE chaitanya (12 years ago)

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chaitanya  (12 years ago)

In the given word, we treat the vowels IEO as one letter.
Thus, we have DRCTR (IEO).
This group has 6 letters of which R occurs 2 times and others are different.
Number of ways of arranging these letters = 6!/2! = 360.
Now 3 vowels can be arranged among themselves in 3! = 6 ways.
Required number of ways = (360x6) = 2160.

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amreen  (12 years ago)

vowels are (ieoa) and we treat them as one word....thus we have drctrc(ieoa) no. of ways arranging this 7 words are as 7!/(2!)(2!) as r and c are coming 2 times so it is 1260 ways....also vowels can arranged among themselves as 4! and it is 24 ways
so total ways of arranging no. so that vowel are always 2gether is (1260*24)=30240

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Aman  (12 years ago)

Good observation by Vignesh.

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