Suppose we have a standard chess set, throw away the pawns, and consider only White's pieces (in other words, two identical rooks, two identical bishops, two identical knights, and a king and queen). We will place them on the first rank of the board, with one piece per square. The picture shows the standard way of placing the pieces, but below we will consider other ways. (i) How many possible distinct configurations of pieces are there? (ii) If we insist that the bishops must be on different-colored squares, how many possible distinct configurations are there? (iii) Suppose that we only consider configurations where the bishops are on different-colored squares and the king is between the two rooks (but not necessarily adjacent to either of them). How many possible distinct configurations are there