MCR Problem of the Week, March 17, 2024 Edition

devourer has $10$ chess pieces: $1$ King, $2$ Queens, $2$ Rooks, $2$ Bishops, and $3$ Knights. He wants to place these pieces in a row of $10$ alternating dark and light squares (see diagram below), one piece per square, such that the following two constraints are followed:

1. The two Bishops must be placed on different color squares. That is, one Bishop on a light square and the other on a dark square
2. The King must be placed between the two Rooks. Other pieces are allowed to be placed between the King and Rooks but there must be a Rook somewhere on each side of the King

Assuming that pieces of the same type are identical, determine the number of different ways devourer can arrange the pieces.

Diagram: