If there is one type of problem that people almost universally revile, it is combinations and permutations. I have a couple of theories for this unfavorable response. First off, most of us do not learn how to do this in school. Or, if we did, it was only a basic lesson in a high school math class, and has since likely receded deep into the fog of adolescence. Really, the first time we see it is when we are prepping for the GRE.
Compounding this problem is my other theory as to why this concept is so feared and loathed. Instead of teaching the concept, most books start off with two cumbersome formulas. The math can be needlessly complex, so that students spend more time crunching numbers than they do understanding when a problem requires combinations or permutations.
While I cannot rescue any moribund memories from junior year math class, I can offer a pragmatic approach to my second theory: take those formulas and flush them down the toilet. Okay, not literally, but you get the sentiment. Instead, I am going to teach you a far more effective approach in dealing with combinations and permutations; one, I hope, that will make you actually enjoy doing these problems.
So, years from now, when your GRE days are long behind you, you will vividly, and maybe even fondly, look back on combinations and permutations. Okay, fine…that may be asking too much. But, I am sure you will find my approach to dealing with combinations and permutations helpful.
Introduction to Combinations Video + Practice Problem:
A committee of three is to be chosen from six. How many unique committees result?
(A) 20 (B) 40 (C) 60 (D) 105 (E) 120
Introduction to Permutations: