  Given sets X and Y of positive integers and a permutation sigma = sigma_1,
sigma_2, ..., sigma_n in S_n, an X,Y-descent of sigma is a descent pair sigma_i
> sigma_{i+1} whose "top" sigma_i is in X and whose "bottom" sigma_{i+1} is in
Y. We give two formulas for the number P_{n,s}^{X,Y} of sigma in S_n with s
X,Y-descents. P_{n,s}^{X,Y} is also shown to be a hit number of a certain
Ferrers board. This work generalizes results of Kitaev and Remmel on counting
descent pairs whose top (or bottom) is equal to 0 mod k.
