>>納n=1,m](n*C(m,n)*P(m,n)*P(l-m,m-n)/P(l,m))=m^2/l

微妙な処はあるが、Mathematica返しだと、
Simplify[Sum[
n Binomial[m, n] FactorialPower[m, n] FactorialPower[l - m,
m - n], {n, 1, m}]/FactorialPower[l, m] // FunctionExpand,
Assumptions -> Element[m, Integers]]

->m^2/l

だが?