2016 UNCO Math Contest II Problems/Problem 9

Problem

Chess Masters

(This should not be in intermediate combinatorics; it makes use of some very obvious basic knowledge of combinatorics) Four identical white pawns and four identical black pawns are to be placed on a standard 8 × 8, two-colored chessboard.

How many distinct arrangements of the colored pawns on the colored board are possible?

No two pawns occupy the same square. The color of a pawn need not match the color of the square it occupies, but it might. You may give your answer as a formula involving factorials or combinations: you are not asked to compute the number.

Solution

There are arrangements of the colored pawns on the standard board.