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≤ l<m are fixed integers and
n→∈fty .
Received August 1, 1998, and in revised form December 15, 1998.