How many ways are there to place a set of chess pieces on the first row of chessboard. The set consists of a king, a queen, two identical rooks, knights and bishops ?
Anonymous:
how manyre hings r the
i think 8 factorial
i havent get right answer yet
u r closer at least
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Answered by
8
Thank you for asking this question from us. It is believed that chess is originated from India and in ancient India, Camel/Bishop, Elephant/Rook, and Horse/Knight are used in the war. There are 5040 ways to place a set of a king, a queen, two identical rooks, knights and bishops on a chessboard. It can be proved as:
If we have to place n things in which a, b and c are identical, then possible ways of arrangement will be n!/(a! x b! x c!).
As 2 pieces of bishop, knight and rook are identical, so the possible ways will be:
8!/(2! x 2! x 2!) - 5040
If we have to place n things in which a, b and c are identical, then possible ways of arrangement will be n!/(a! x b! x c!).
As 2 pieces of bishop, knight and rook are identical, so the possible ways will be:
8!/(2! x 2! x 2!) - 5040
Answered by
2
Thank you for asking this question.
Here is your answer:
The first King could be on a corner square(4 ways), leaving 60 other squares for the next King.
The first King could be on a edge square(24 ways), leaving 58 other squares for the next King.
The first King could be on a central square(36 ways), leaving 55 other squares for the next King.
This will double count the configurations, so we have (4×60+24×58+36×55)/2=1806.
If there is any confusion please leave a comment below.
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