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In how many ways can the letters of a word 'G M A T I N S I G H T' be

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In how many ways can the letters of a word 'G M A T I N S I G H T' be  [#permalink]

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New post 24 Feb 2017, 05:52
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

54% (03:04) correct 46% (02:41) wrong based on 73 sessions

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In how many ways can the letters of a word 'G M A T I N S I G H T' be arranged to form different words such that vowels occupy the odd numbered positions in the word (whether the word makes sense or not)?

A) 11!
B) 15*8!
C) 8!
D) 8!/(2!*2!)
E) 11!/(2!*2!*2!)

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Re: In how many ways can the letters of a word 'G M A T I N S I G H T' be  [#permalink]

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New post 24 Feb 2017, 06:52
GMATinsight wrote:
In how many ways can the letters of a word 'G M A T I N S I G H T' be arranged to form different words such that vowels occupy the odd numbered positions in the word (whether the word makes sense or not)?

A) 11!
B) 15*8!
C) 8!
D) 8!/(2!*2!)
E) 11!/(2!*2!*2!)

Source: http://www.GMATinsight.com


Hi,

Word is 'G M A T I N S I G H T'
Total positions = 11
Odd positions = 6 ,Vowels: A, I, I
Repetitive letters: G - 2, T - 2, I - 2,

'A' can be placed in any of the 6 odd positions - 6 ways
'I' can be placed in any of the remaining 5 odd positions - 5 ways
'I' can be placed in any of the remaining 4 odd positions - 4 ways

Total ways to arrange vowels = 6*5*4/2 = 60 ways ('I' repeats twice, so we need to divide it by 2).

AND
Remaining eight consonants can be arranged in \(\frac{8!}{2!\times 2! }\)

Total number of words = \(60 \times \frac{8!}{4}= 15 \times 8!\). Answer: B

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Re: In how many ways can the letters of a word 'G M A T I N S I G H T' be  [#permalink]

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New post 09 Jul 2018, 21:42
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Re: In how many ways can the letters of a word 'G M A T I N S I G H T' be &nbs [#permalink] 09 Jul 2018, 21:42
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