  Let $f(j,k,n)$ denote the expected number of $j$-faces of a random
$k$-section of the $n$-cube. A formula for $f(0,k,n)$ is presented, and for
$j\geq 1$, a lower bound for $f(j,k,n)$ is derived, which implies a precise
asymptotic formula for $f(n-m,n-l,n)$ when $1\leq l<m$ are fixed integers and
$n\to\8$.
