Combinations : Quant Question Archive [LOCKED]
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# Combinations

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Current Student
Joined: 21 Oct 2009
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27 Oct 2009, 22:29
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

This question doesn't come from GMAT text book. It just popped up in my mind during my study.
Given a set of letters (A,B,C), how many combinations of 4 letters are there, using both A and C at least once? You don't have to use all of them. Besides, (AACC), (CCAA),(ACAC),(CACA),(CAAC) and (ACCA) are all considered same.

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Joined: 02 Sep 2009
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Kudos [?]: 93149 [2] , given: 10553

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27 Oct 2009, 23:54
2
KUDOS
Expert's post
yuskay wrote:
This question doesn't come from GMAT text book. It just popped up in my mind during my study.
Given a set of letters (A,B,C), how many combinations of 4 letters are there, using both A and C at least once? You don't have to use all of them. Besides, (AACC), (CCAA),(ACAC),(CACA),(CAAC) and (ACCA) are all considered same.

Let me put it this way if I got it right:

We have 3 letters A,B and C. We want to form 4 letter combination from this letters, with condition that:
1. Order doesn't matter.
2. We should use at least once A and C, but not necessarily B.
How many such combinations are possible?

If it's so then, let's fix TWO letters AC, as they always should present.

We can easily right down all the possibilities.
Fixed AC as we must use them and any 3 left letter from the set:
ACAA
ACAB
ACAC
ACBB
ACBC
ACCC
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Current Student
Joined: 21 Oct 2009
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Kudos [?]: 7 [0], given: 4

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28 Oct 2009, 01:47
Bunuel, thank you!
Re: Combinations   [#permalink] 28 Oct 2009, 01:47
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