  In earlier work the authors obtained formulas for the probability in the
asymmetric simple exclusion process that the $m$th particle from the left is at
site $x$ at time $t$. They were expressed in general as sums of multiple
integrals and, for the case of step initial condition, as an integral involving
a Fredholm determinant. In the present work these results are generalized to
the case where the $m$th particle is the left-most one in a contiguous block of
$L$ particles. The earlier work depended in a crucial way on two combinatorial
identities, and the present work begins with a generalization of these
identities to general $L$.
