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 $\frac{64!}{56!4!4!}$ arrangements of the colored pawns on the standard board.

See also

2016 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions