2024 AIME II Problem 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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.