I think you don't have correctly understood the kata. The description says:

In other words we must find x such as n choose x = m (1) for a given m and a given n

You have to solve an equation not an inequation. 48 choose 11 gives 22595200368, not 6540715897 and 34 choose 4 gives 46376 not 5985.

BTW thanks for the links!