Chess board a b c d e f g h 8 × 8 permutationπof[m × 7 6 X 宣 6 {(i,π()|i∈[n 5 X 5 4 X 4 3 × X “A placement of 宣 1 non-attacking rooks'” b d e g h forbidden positions B[n]x In] derangement: B={(i,)|i∈[m}Chess board permutation ￾ of [n] {(i, ￾(i)) | i ￾ [n]} “A placement of non-attacking rooks” forbidden positions B ⇥ [n] ￾ [n] derangement: B = {(i, i) | i ￾ [n]}