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.

Answers were Sorted based on User's Feedback

How many ways are there of arranging the sixteen black or white pieces of a standard international..

Answer / 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

How many ways are there of arranging the sixteen black or white pieces of a standard international..

Answer / billy busse

The explanation above is correct, but the number they gave
as an answer is not written in proper syntax

64,864,800 ways

Is This Answer Correct ?    0 Yes 3 No

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