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Director
Joined: 03 Jul 2003
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In how many ways can the letters of the word "permutations" [#permalink]
 07 Jan 2004, 09:20
In how many ways can the letters of the word "permutations" be arranged such that order of vowels remains unchanged?
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Director
Joined: 05 May 2003
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What is the official answer ??
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SVP
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P E R M U T A T I O N S
x E x x U x A x I O x x
If we dont want to change the order then there 4 possible ways for EUAIO to occupy 12 places as follows
ExxUxAxIOxxx
xExxUxAxIOxx
xxExxUxAxIOx
xxxExxUxAxIO
Among available 7 places we need to arrange 7 letters with letter T repeating twice.
So we have 7!/2!
Total ways = 4 * 7! / 2! = 10080
What is the official answer ?
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Senior Manager
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The problem just says that the order of the vowels must be respected. So it could be euaioxxxxxxx, xeuaioxxxxxx, xexuxaxixoxx, etc...
In that case I think the answer 12! divided by 2! (because of the double t) and 5! (to eliminate the different orders of the 5 vowels).
That is 12!/(2!*5!)
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SVP
Joined: 30 Oct 2003
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I agree with you martin.
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