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In a particular chess variant, the pieces are placed randomly in a row behind the pawns. Determine the number of possible ways a player’s pieces can follow all of these rules:  There are 8 pieces (a King, a Queen, two Rooks, two Knights, and two Bishops)  The two Bishops must go on opposite colors squares (Note: squares alternate between dark and light)  The King must go between the two Rooks (though the other pieces can also be between them)  The Queen and Knights have no restrictions

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Let's see... the dark-squared bishop can go on any of $4$ squares, as can the light-squared bishop. Then the queen has $6$ squares left it can go on and the knights have $\binom{5}{2}=10$ possible placements. After that the placement of the king and the rooks is fixed so there are $$4\times4\times6\times10=960$$ ways to configure each player's pieces.

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  • $\begingroup$ thank you so much. :) $\endgroup$
    – teck
    Commented Mar 11, 2020 at 6:37

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