How many ways are there of arranging the sixteen black or
white pieces of a standard international chess set on the
first two rows of the board?
Given that each pawn is identical and each rook, knight and
bishop is identical to its pair.
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Answer Posted / guest
6,48,64,800 ways
There are total 16 pieces which can be arranged on 16
places in 16P16 = 16! ways.
(16! = 16 * 15 * 14 * 13 * 12 * ..... * 3 * 2 * 1)
But, there are some duplicate combinations because of
identical pieces.
? There are 8 identical pawn, which can be arranged
in 8P8 = 8! ways.
? Similarly there are 2 identical rooks, 2 identical
knights and 2 identical bishops. Each can be arranged in
2P2 = 2! ways.
Hence, the require answer is
= (16!) / (8! * 2! * 2! * 2!)
= 6,48,64,800
| Is This Answer Correct ? | 1 Yes | 2 No |
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