@habibkhan , Is it same as your's or it is wrong-
E =$ \frac{ 1 * C(m,1) * C(N-m, n-1))}{C(N,n)}+ \frac{ 2 * C(m,2) * C(N-m, n-2))}{C(N,n)}$
$+ \frac{ 3 * C(m,3) * C(N-m, n-3))}{C(N,n)} + \frac{ 4 * C(m,4) * C(N-m, n-4))}{C(N,n)} + .....$
$+ \frac{ m * C(m,m) * C(N-m, 0))}{C(N,n)}$.