# A probability problem by soumyaranjan ram

Probability Level 4

On a large $999 \times 999$ board, each cell is colored either white or black.

Define a coordinated triple of cells $(C_1, C_2, C_3 )$ as the formation such that

• $C_1$ and $C_2$ are in the same row;
• $C_2$ and $C_3$ are in the same column;
• $C_1$ and $C_3$ are white;
• $C_2$ is black.

What is the maximum number of coordinated triples? Enter your answer as the last three digits of that maximum.

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