Number of ways to place chess figures on one line of chess board How many ways to place chess figures of one color (2 rooks, 2 knights, 2 bishops, 1 king and 1 queen) on one line of chess board such that 2 bishops are located on the cells with different color and the king is located between 2 rooks? Number of ways to place bishops on the cells with different color is 12. I made some by-hand calculations to get the number of ways to place the king between 2 rooks on 6 remaining cells and guess it equals 60. So overall number is 720. Am I right? Thanks!

The bishops have $16$ ways-four light squares times four dark squares. Then if you choose three of the remaining six squares (${6 \choose 3}=20$ ways) you know where the king goes. Now choose one of the three squares for the queen.