4 Player Board Game

Probability Level 5

Four players are playing a game involving choosing 1×11\times1 squares on a grid of size 3×83 \times 8. Each player chooses a random square on the grid, then all players reveal their choices and a token is placed in the center of each of these squares. The probability that the tokens form the vertices of a non-degenerate rectangle can be expressed as ab\frac{a}{b} where aa and bb are coprime positive integers. What is the value of a+b?a + b?

Details and assumptions

Players are allowed to have selected the same squares. There is no restriction on their choices.
A degenerate rectangle has 0 area.
Squares are rectangles.


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