limn→∞ ncrmnr1−mnn−r equals

limn→∞n Crmnr1−mnn−r=limn→∞ n(n−1)(n−2)…(n−r+1)r!⋅mrnr1−mn−nm−(n−r)×mn=limn→∞ n(n−1)(n−2)…(n−r+1)nrmr=limn→∞ 1−mn−nm1−rn(−m)=(1−0)(1−0)…(1−0)r!mre−m=e−mmrr!