Like permutations, combinations is a concept that unnecessarily frightens students: there are very few, if any combination questions, on a test that a student may have to take the SAT for an entire year to even see one of these question types (the SAT is administered eight times a year).
Why then even talk about combinations? Well, to make the announcement above (basically, don’t sweat it). But if you want to make sure you have all your math bases covered, then read on.
Rule #1 Combinations is about choosing
The ‘C’ in combinations equals ‘c’hoosing. A silly mnemonic perhaps, but one that will hopefully help you tell the difference between permutations and combinations.
Mark has a brown, white, blue, red, and black T-shirt. If he wants to pack two T-shirts for a weekend trip, then how many different T-shirts can he take with him?
Notice that, unlike a permutation question, Mark is not arranging his shirts in an order. He is choosing two to take with him. We do not care whether his red T-shirt is packed on top of his white T-shirt. This ordering (or arrangement) is key to a permutation problem but does not relate to a combination problem.
So now that we know we are dealing with a combination problem (after all this is a combination post), we need to use the following formula:
Notice how we can easily cancel out the 3 x 2 x 1 from both the numerator and the denominator. This leaves us with 5 x 4/2 = 10. Therefore, Mark can take a total of 10 shirts.
Don’t fret combinations. They are very likely to show up on the test, and when they do, they are no more difficult than the question above.