Question 9
There is a collection of $25$ indistinguishable white chips and $25$ indistinguishable black chips. Find the number of ways to place some of these chips in a $5 \times 5$ grid such 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, and
• any additional chip placed on the grid would violate one or more of the previous two conditions.
• each cell contains at most one chip
• all chips in the same row and all chips in the same column have the same color, and
• any additional chip placed on the grid would violate one or more of the previous two conditions.