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

Note: ^{M}C_{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.

Many pairs are possible, in terms of the given conditions.

For a comprehensive list of all these pairs together with the methods for deriving them, refer to the solution submitted by Daniel in this location, and the solution submitted by Charlie in this location.

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