Determine all possible pair(s) (M, X) of positive integers, with M - 1 > X > 1, such that the decimal representation of ^MC_X consists of non leading zeroes and contains each of the digits 0 to 9 exactly once.

Note: ^MC_X is the number of X-element subsets (the X-combinations) of an M-element set, that is the number of ways that X things can be 'chosen' from a set of M things.

My first thought on seeing the solutions:  Wow there are a lot of solutions.

My second thought: most of them have x=2.  This shouldn't be surprising.  The interesting solutions are the other two.

Posted by Jer on 2009-04-29 13:35:09