MathDB

There is a collection of

25

indistinguishable black chips and

25

indistinguishable white chips. Find the number of ways to place some of these chips in

25

unit cells of a

5 \times 5

grid so that:
[*]each cell contains at most one chip, [*]all chips in the same row and all chips in the same column have the same color, [*]any additional chip placed on the grid would violate one or more of the previous two conditions.

Problem Statement