The twelvefold way f:N→M n balls are put into m bins balls per bin: unrestricted ≤1 ≥1 n distinct balls, m distinct bins mn (m)n n identical balls, m distinct bins () m (a-） n distinct balls, fn≤m m identical bins 0 ifn>m n identical balls, 1ifn≤m m identical bins 10 if n>mballs per bin: unrestricted ≤ 1 ≥ 1 n distinct balls, m distinct bins n identical balls, m distinct bins n distinct balls, m identical bins n identical balls, m identical bins f n balls are put into m bins : N ￾ M mn (m)n ￾m n ⇥ ￾ 1 if n ￾ m 0 if n>m ￾ 1 if n ￾ m 0 if n>m The twelvefold way ￾n ￾ 1 m ￾ 1 ￾￾ ⇥ m n ⇥⇥