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Chris Lele

SAT Math Basics – Permutations

The name alone conjures up something arcane and impenetrable (two good SAT vocab words!). Once students learn the concept, it only intensifies their fears. All that said about how scary permutations are, by keeping your cool, you will be able to handle this tough concept, and show the SAT who is boss.


Number One Thing You Have to Know: Arrangement = Permutation

If I were the God of math and could decree the way things should be, I would call permutations arrangements. Of course that is because I would be a nice math God, and would want to make math seems as easy possible. It is not that mathematicians are evil math Gods, their wrath raining down upon us in the form of tongue-twisting concepts. Simply put, every field has its jargon (good SAT word!) and if you want to learn that field you have to know the lingo.

Anyhow, I’m here to make things easier.

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Rule #1: Whenever you are dealing with the total number of ways things can be arranged, use permutations.

If you have five students sitting in a row and want to see how many ways there are to arrange them, use permutations. With this example all you would have to do is take the number of things being arranged (five students), and put a (!) next to it. This sign is called a factorial and means the following:

5! = 5 x 4 x 3 x 2 x 1 = 120.

An easy way to think of how to deal with factorial is what I call the Space Shuttle Countdown: Whatever number you are ‘factorial-ing,’ countdown a number at a time—as though you are the guy announcing the takeoff of the space shuttle. So 10! = 10 x 9 x 8… x 3 x 2 x 1 = Takeoff! Well, actually a very large product.

The good news is the factorials on the SAT usually won’t be over 5!.



Whenever you are asked the find the total number of ways you can arrange something, use permutations (and don’t forget the factorial!).


About Chris Lele

Chris Lele is the GRE and SAT Curriculum Manager (and vocabulary wizard) at Magoosh Online Test Prep. In his time at Magoosh, he has inspired countless students across the globe, turning what is otherwise a daunting experience into an opportunity for learning, growth, and fun. Some of his students have even gone on to get near perfect scores. Chris is also very popular on the internet. His GRE channel on YouTube has over 10 million views. You can read Chris's awesome blog posts on the Magoosh GRE blog and High School blog! You can follow him on Twitter and Facebook!

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