given sets $x$ and $y$ of positive integers and a permutation $\sigma = \sigma_1 \sigma_2 \cdots \sigma_n$, an $x,y$-\emph{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 $k$. (this is joint work with jeff remmel.)