Chess board a b c d e f g h 8 × 8 Bc[ml×[ml 7 × 7 6 X 6 5 X 5 Tk· 4 4 3 × of ways of placing k 2 X 2 宣 non-attacking rooks in B a b g h No of placements of n non-attacking rooks m N0=(-1)k(n-)川 k=0Chess board B ⇥ [n] ￾ [n] N0 : # of placements of n non-attacking rooks rk : # of ways of placing k non-attacking rooks in B N0 = ￾ n k=0 (￾1)krk(n ￾ k)!