Los Angeles Math Circle

4/13 -- High School I Circle: Counting (Prof. Po-Shen Loh, Carnegie Mellon University)

How hard can it be to count? The answer to that question may depend on how much stamina you have. It might, for example, take an awfully long time to count how many 125-element subsets there are of {1, 2, ..., 250} by simply listing all of them. There are faster ways to calculate this number, but even then, at first glance it may appear to require a substantial amount of computation in order to determine even the last digit of "250 choose 125". In this talk, we will find this last digit, and explore some related topics. (Hint: the last digit is not zero - that would be too easy!)