Hey Winnie,
You know, I think the best way to get started on permutations, particularly, is to think them through yourself and not just to read what someone else has written on it. If you can teach yourself the fundamentals through logic, then the advanced applications and time-saving methods will make exponentially more sense.
So think about this: Say there were five of us running a race, and I wanted to know how many different gold-silver-bronze medal finishes there could be. How would we calculate that?
Well, each of the five of us could win. So there are five potential gold-medal winners.
For each person who has won gold, there are four people left who could win silver.
And for each gold-silver pairing there are three people left to win bronze.
If you were to draw this out you could probably see even clearer why we'll then multiply 5*4*3.
For person A to win gold, there are then 4 people left for silver: B, C, D, or E. And say that the pairing is AB, then there are three left: C, D, or E. If you draw all of those out, you'll see how the tree branches out. For each of the 5 first-place possibilities, there are four seconds. And for each of those, there are three thirds. Add all those possibilities up and you get 5*4*3 = 60.
If you approach some of the more average-level problems this way and really think them through, you'll start to see why the math holds and not just try to memorize the math. Honestly, a lot of GMAT permutation/combination problems can be solved simply by listing out the possibilities; it's more time-consuming than you'd probably want and there are plenty of problems for which you can't do that, but especially in practice if you let yourself struggle through it conceptually then you'll understand why the math works and you'll have an easier time ramping up to the really hard stuff.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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