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:
Next up:
The Difficulty of Context: Combinations and Permutations Practice Questions
Combinations and Permutations Practice Questions and Video Explanations
Three Challenge Combinations/Permutations Problems
120 is the answer
The answer is simply 20.
I just had a question about the semantics for the practice question regarding the committee. It says how many UNIQUE committees can be formed, so to me, this means that the order does matter. I understand the difference between choosing to solve problems with either a permutation or a combination but the word unique here makes me think that the order of ABC and BCA don’t mean unique and therefore the order would matter and would prompt me to solve the question with a permutation. Is this thinking wrong? I guess I’m confused!
Hi Mandy,
Interesting point! I can see your logic–once people are in the committee they can form different unique committees based on their position with the committee. The thing is the question doesn’t give any specific information about within the committee, if indeed there are even any subdivisions within the committee. Therefore, we have to take the language to mean different committees of people.
Hope that helps clear things up :)!
Thanx….that is so good!
Hi Chris, Thanks for your very lucid explanation. However, i am surprised to hear that it’s just a “mere lesson” in high school there. In India , its been rigorously tought along with probability for two years and It’s always been my favorite topic as it does not rely too much on your knowledge of algebra and geometry. So I see p&c (and probability to an extent) more of a logic problems than math.
Anupam
Hi Anupam,
It’s true – I teach SAT as well and most students have only a rudimentary knowledge of p&c. Some simply never go over the concept at all. Not to get up on a giant soapbox here, but sometimes I lament the way math is taught here. Students become very good at following steps, thereby getting the requisite A. But the actual logic of how to approach math problems, whether they deal with probability or integer properties, is given very little emphasis (hence, the many GRE students who were A and B students in math but who struggle, at least at first, on the GRE quant section).
I’m glad you enjoyed my post!