Latest iGate Aptitude Question SOLUTION: In how many ways can the letters of a word \'ENGINEERING be arranged such that vowels DO NOT together from m4maths

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In how many ways can the letters of a word 'ENGINEERING be arranged such that vowels DO NOT together from m4maths

Asked In iGate charan (10 years ago)

Solved RAKESH Read Solution (4)

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RAKESH  (10 years ago)

ENGINEERING
total 11 letters
E=3,N=3,G=2,I=2,R=1,

Total no. of ways = 11!/3!3!2!2! = 277200

when vowels come together = (EEEII)NNNGGR => 7!/3!2! * 5!/3!2! = 4200

No. of ways when vowels DO NOT together = 277200 - 4200 = 273000

Is this solution Helpfull? Yes (27) | No (1)  

RAKESH  (10 years ago)

ENGINEERING
total 11 letters
E=3,N=3,G=2,I=2,R=1,

Total no. of ways = 11!/3!3!2!2! = 277200

when vowels come together = (EEEII)NNNGGI => 7!/3!2! * 5!/3!2! = 4200

No. of ways when vowels DO NOT together = 277200 - 4200 = 273000

Is this solution Helpfull? Yes (4) | No   

M Sai Harish  (10 years ago)

In ENGINEERING word should be arranged such that vowels donot come together so Total no of Combinations-no of combinations such that vowels come together will be answer. So Total no of Combinations = 11!/(3!*3!*2!*2!)=277200 because 3E, 3N, 2G, 2I and No of Combinations where vowels come together = {7!/(3!*2!)}*{5!/(3!*2!)}[NNNGGR(EEEII)]=4200. Therefore in ENGINEERING word should be arranged such that vowels donot come together = 277200-4200=27300.

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charan  (10 years ago)

a.273500 b.273600 c.273000 d.277330

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