Latest self Aptitude Question SOLUTION: In how many ways can the letters of the word 'ORANGE' be arranged so that none of the vowels are adjacent to each other? Ops: A. 144 B. 720 C. 360 D. 576

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(#M40018387) SELF question APTI Keep an EYE

In how many ways can the letters of the word 'ORANGE' be arranged so that none of the vowels are adjacent to each other?
Ops: A. 144
B. 720
C. 360
D. 576

vikash kumar shukla (11 years ago)

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IFFAT IRAM  (11 years ago)

total no. of ways in the word can be arranged = 6! ways
no. of ways it can be arranged with vowels kept together = 4! * 3! ways
no. of ways it can be arranged so that no vowels are together 6! - (4! * 3!)=576

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Karan  (11 years ago)

144

There are 6 letters and 6 positions.
As per condition
vowels can be placed at 135,136,146 and 246 positions only.
In between those positions , 3 vowels can be arranged 3! ways and 3 consonants can be arranged in 3! ways.

so total ways in which the letters of the word 'ORANGE' be arranged so that none of the vowels are adjacent to each other = 4*3!*3!= 4*6*6=144

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