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Combinations

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Current Student
Joined: 21 Oct 2009
Posts: 41
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Kudos [?]: 4 [0], given: 4

Combinations [#permalink]  27 Oct 2009, 22:29
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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Math Expert
Joined: 02 Sep 2009
Posts: 28352
Followers: 4486

Kudos [?]: 45486 [2] , given: 6762

Re: Combinations [#permalink]  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
_________________
Current Student
Joined: 21 Oct 2009
Posts: 41
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Kudos [?]: 4 [0], given: 4

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