Special Coin Placement

Probability Level 4

Three coins are randomly placed into different positions on a 4×104 \times 10 grid. The probability that no two coins are in the same row or column can be expressed as ab\frac{a}{b} where aa and bb are coprime positive integers. What is the sum of a+ba + b?

Details and assumptions

The coins are placed into different positions which means that no 2 coins are placed in the same square.

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