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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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SVP
Joined: 08 Jul 2010
Posts: 2115
Location: India
GMAT: INSIGHT
WE: Education (Education)
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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24 Feb 2017, 06:52
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Difficulty:

65% (hard)

Question Stats:

64% (02:33) correct 36% (01:53) wrong based on 45 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!)

Source: http://www.GMATinsight.com

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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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24 Feb 2017, 07:52
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

Thanks.
Re: In how many ways can the letters of a word 'G M A T I N S I G H T' be   [#permalink] 24 Feb 2017, 07:52
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