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by knight247 » Sat Jun 25, 2011 4:53 am
if the letters of the word MANAGEMENT are arranged in different orders, in how many of the arrangements will the vowels be in even positions?
(A)2880
(B)5400
(C)17280
(D)21600
(E)86400

OA is [spoiler](B) [/spoiler]

Detailed explanations would be appreciated
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by vikram4689 » Sat Jun 25, 2011 5:17 am
5 odd positions & 5 even positions

6 non-vowel letters - M,M,G,T,N,N
4 vowel letters = A,A,E,E

5 even places can be arranged in 5! ways and other 5 odd places can be arranged in 5! ways. But in this case 1 consonant has to be on EVEN position and for this there are 6 options as any one of the consonants can be there.

So no. of ways = 5!*5!*6 = 86400

Now there are repetitions of 2M,2N,2A,2E

So divide by 2*2*2*2
Total no of ways = 86400/16 =5400
Last edited by vikram4689 on Sat Jun 25, 2011 9:42 am, edited 1 time in total.
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by winniethepooh » Sat Jun 25, 2011 5:54 am
When did N become a vowel?
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by Tani » Sat Jun 25, 2011 7:50 am
N is not a vowel. In fact, if it were, the answer would be zero because there would be 6 vowels and only 5 even positions.
Tani Wolff
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by knight247 » Sat Jun 25, 2011 8:17 am
Tani,
Can we plz have your solution to the question.

Thanks
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by winniethepooh » Sat Jun 25, 2011 8:29 am
hey the answer by vikram is right,if I am not wrong.
I think that's the OA, isn't'it?
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by vikram4689 » Sat Jun 25, 2011 9:43 am
Sry guys, changed my solution above to correct the typo.
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