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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!

user144765
  • 730
  • Do you mean the king needs to be next to the rooks, or just somewhere in between? If next to, it is a duplicate. My answer (and it appears yours) assumes somewhere in between. – Ross Millikan Nov 14 '14 at 05:01
  • I meant "somewhere in between two rooks" – user144765 Nov 14 '14 at 05:05
  • The old question was somewhat vague, and the asker may have been asking about positions where the rooks were right next to the kings, but this answer also gave the number of positions without that artificial requirement. – bof Nov 14 '14 at 05:07

1 Answers1

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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.

Ross Millikan
  • 374,822