I ain't gonna lie: these problems are frigging hard, and I get questions on them all the time, both from academic students and SAT prep. The obvious problem is that the formulas are just plain confusing on their own; but worse is that it's really confusing to figure out which problems are permutations and which are combinations. And that's all just for class. Then you start prepping for the SAT and you realize that all the nCr and nPr stuff you worked so hard on is basically useless because the SAT people appear to pride themselves on ruining your life. And they are! Have no fear, though, I'll show you a no-formula technique that works for most SAT combinatorics questions, and even a few advanced moves that work on the hardest ones.
Intro to Permutations & Combinations
This video starts with the differences between permutations and combinations, and shows you how to spot which type of problem you're looking at. Then I work a bunch of problems of each type, showing you how to list out all the possible combinations and permutations in an organized way, such as ABC, CBA, BCA, etc. Stay organized!
Permutations: a closer look
In this video we get into the nitty gritty of nPr notation: what it's for and how to use it, including a bunch of example permutation problems about student council, sports teams, and family portraits. Also discussed are Circular Permutations, which is a gotcha question a lot of teachers use which applies only to items in a circle on something that rotates.
Combinations: a closer look
We touched on combinations in the intro video, but now we'll learn nCr notation: what it's for and how to use it. And since there's so much confusion out there about combinations vs the permutations of the last video, this video focuses on how combinations are different. Example problems include pizza toppings, student committees, and baseball batting order.
Tricky Permutation and Combination Problems for SAT
This video is all about doing tricky SAT combinatorics problems without using any formulas. Instead, we'll just make blanks, then fill in numbers and multiply in a sort of truncated factorial technique. Examples include how many ways you can rearrange the letters of a word, form a committee of both parents and teachers, compose a password, and limited seating arrangements.
Binomial Expansions & Pascal's Triangle
These are problems like "Find the third term of the binomial expansion of (x+2)12" which would take forever to FOIL, but which can be done relatively painlessly (notice the word relative) using the combination formula nCr. Whatever you do, remember n-1: if you're looking for the sixth term, you plug in five for "r"!
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)