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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

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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Source: Beat The GMAT — Problem Solving | Sat Jun 25, 2011 4:53 am

vikram4689: Legendary Member; Posts: 1325; Joined: Sun Nov 01, 2009 6:24 amFollowed by: 14 members; Thanked: 105 times

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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winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pmFollowed by: 2 members; Location: Arlington, MA.; Thanked: 27 times

by winniethepooh » Sat Jun 25, 2011 5:54 am

When did N become a vowel?

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Tani: Legendary Member; Posts: 1255; Joined: Fri Nov 07, 2008 2:08 pmFollowed by: 90 members; Location: St. Louis; Thanked: 312 times

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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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Sat Jun 25, 2011 8:17 am

Tani,
Can we plz have your solution to the question.

Thanks

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winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pmFollowed by: 2 members; Location: Arlington, MA.; Thanked: 27 times

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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vikram4689: Legendary Member; Posts: 1325; Joined: Sun Nov 01, 2009 6:24 amFollowed by: 14 members; Thanked: 105 times

by vikram4689 » Sat Jun 25, 2011 9:43 am

Sry guys, changed my solution above to correct the typo.

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