In how many ways can the letters of the word double be : PS Archive
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# In how many ways can the letters of the word double be

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Manager
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In how many ways can the letters of the word double be [#permalink]

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31 May 2005, 22:40
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In how many ways can the letters of the word â€˜doubleâ€™ be rearranged such that the order in which the vowels appear in the word does not change?
Manager
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01 Jun 2005, 00:14
chris, can you explain more.

what's the difference with, "in how many ways can the word 'mobile' be rearanged to form 6 letter words such that the vowels take odd positions"?

in the mobile thing, it's 3! * 3!

why don't we apply the same thing to 'double' and then subtract 3!.

I guess am missing a piece of the logic!
SVP
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01 Jun 2005, 00:39
It's 6!/3!

6! words can be formed with the word 'double', taking all letters (without any condition).

Now, in all possible words above, 3 vowels will be in 3! number of orders & we want all words in only one order out of 3! orders. So, 6!/3! ways.
VP
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01 Jun 2005, 00:45
Dan wrote:
chris, can you explain more.

what's the difference with, "in how many ways can the word 'mobile' be rearanged to form 6 letter words such that the vowels take odd positions"?

in the mobile thing, it's 3! * 3!

why don't we apply the same thing to 'double' and then subtract 3!.

I guess am missing a piece of the logic!

in the question with the word double, you have 6 spaces _ _ _ _ _ _ . you can place the vowels in much more places as you can place them in the question about the word mobile. o u e _ _ _ or o _ u e _ _ or _ _ ou _ e and so on.its only important that the order is o u e. in the second question you have again 6 spaces and you can place the vowels only on the odd positions. so its o _ i _ e _. the main difference is that in the 2nd quest., you have only 1 way to place the letters with different letters and in the 1st question, there are many ways with different letters. by the way in the double-question you divide by 3! because otherwise o u e as well as e o u would be counted, but ONLY o u e is permitted and so you divide by 3! to get rid of these arrangements.
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01 Jun 2005, 01:14
thanks!

it's as if you're treating the 3-letter 'oue' as one repetitive letter, then you divide by 3! to get rid of 'repetitive' or unwanted arrangements.
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Re: PS- Combo [#permalink]

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01 Jun 2005, 09:53
Dan wrote:
In how many ways can the letters of the word â€˜doubleâ€™ be rearranged such that the order in which the vowels appear in the word does not change?

I too got 120.

First treating oue as a single alphabet we get 4! combinations = 24

now with one of the other letters within the "oue" combination (o_ue,ou_e)we have a total of 3*2*3! combinations = 36

now with two other letters within the "oue" combinations(o_ue,ou_e) we get 3*6*2 combinations = 36

with all the other three leters within the "oue" combination(o_ue,ou_e) we get 24 combinations.

HMTG.
Re: PS- Combo   [#permalink] 01 Jun 2005, 09:53
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# In how many ways can the letters of the word double be

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