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Arran x items from a collection of N

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Manager
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Joined: 15 Jul 2008
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Arran x items from a collection of N [#permalink]

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New post 05 Aug 2008, 06:18
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

[edited once]

Guys,

I am having some confusion over this question

How many 3 letter words (arrangements) can you form with alphabet drawn from aabbbccccdddeefffgg

For such a case is there an expression similar to the one for following case ?..

how many ways can you arrange all of them, answer = 19!/2!3!4!3!2!3!2!

Last edited by bhushangiri on 05 Aug 2008, 07:44, edited 1 time in total.

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Re: Arran x items from a collection of N [#permalink]

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New post 05 Aug 2008, 07:10
I think the way to approach the first question is that you notice that there are only 3 letters to choose from.

So, with three different letters, you can choose from 3 letters for the first space, 3 letters for the second space, and 3 letters for the second space. That's 3x3x3=27.
Since 'aaa' is not possible, then it's 27-1 = 26 arrangements.

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Re: Arran x items from a collection of N [#permalink]

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New post 05 Aug 2008, 07:38
rigger wrote:
I think the way to approach the first question is that you notice that there are only 3 letters to choose from.

So, with three different letters, you can choose from 3 letters for the first space, 3 letters for the second space, and 3 letters for the second space. That's 3x3x3=27.
Since 'aaa' is not possible, then it's 27-1 = 26 arrangements.


Thanks. But i am looking for a more generic expression. Like n!/(a!b!) is for arranging all the given items.

I am editing the question to reflect that possibility also.

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Re: Arran x items from a collection of N [#permalink]

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New post 05 Aug 2008, 08:33
n!/(a!b!....) is the general expression. There's nothing more to it than that.

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Re: Arran x items from a collection of N [#permalink]

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New post 05 Aug 2008, 08:39
rigger wrote:
n!/(a!b!....) is the general expression. There's nothing more to it than that.


But that is only if you arrange all n. Not if you take some from the n and try to arrange.

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Re: Arran x items from a collection of N   [#permalink] 05 Aug 2008, 08:39
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