Hey wydadi,
Great question - I love when people take the time to try to think through alternate methods, and I think you can learn a lot by recognizing why they do or don't work.
One of my favorite strategies for GMAT questions is to test your theory, or try to find a pattern, using small numbers. Usually you'll be able to prove yourself right or wrong, and also be able to understand conceptually WHY you're right or wron,g which leads to much deeper understanding.
Since TRUST has quite a few possibilities (5! = 120, the answer is 5!/2! or 60, and you had 96...way too many possibilities to try to draw out), let's use something smaller - 4 letters with one repeat:
ABCA
We should be able to list all of those out by staying organized and trying new permutations one at a time:
ABCA
ABAC
ACAB
ACBA
AABC
AACB
BCAA
BACA
BAAC
CBAA
CABA
CAAB
There are 12 ways to do it, and we can't come up with any more without just flipping our As, which doesn't give us anything new. 12, also, is consistent with the formula (which it should be, of course): 4!/2! = 12.
Now let's look at your method:
ABC gives you 3! ways to arrange, and then you can put the A in different spots: left of the A, left of the B, left of the C, and right of the C (AABC, AABC, ABAC, ABCA). This should point out a problem, though - the first two are the exact same! So you can see where your method won't work - every few permutations you'll end up with a duplicate spot, so you'll overestimate the number of possibilities.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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