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.

I am kind of comfused during the caliculation. pLease help me.

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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