Four players are playing a game involving choosing positions on a grid of size 3×8. Each player chooses a random position on the grid, then all players reveal their choices and a token is placed on each of the positions. The probability that the tokens form the vertices of a non-degenerate rectangle can be expressed as a/b where a and b are coprime positive integers. What is the value of a+b?

To find the probability that the tokens form the vertices of a non-degenerate rectangle, we need to consider all possible ways in which the tokens can be placed on the grid.

First, let's consider the number of ways to choose the positions for the tokens. Each player has 3 options for the row and 8 options for the column, so the total number of ways to choose the positions is 3^4 * 8^4 = 18,874,368.

Next, let's consider the number of ways in which the tokens can form the vertices of a non-degenerate rectangle. A non-degenerate rectangle can be formed when the two horizontal (or vertical) sides of the rectangle have the same length, and the two vertical (or horizontal) sides have the same length.

For the horizontal sides to have the same length, we need two tokens to be in the same row. Since there are 3 rows, there are C(4, 2) = 6 ways to choose the two positions in the same row. The remaining two tokens can be placed in any of the 2 remaining rows, so there are 2^2 = 4 possible positions for the remaining two tokens.

Similarly, for the vertical sides to have the same length, we need two tokens to be in the same column. Since there are 8 columns, there are C(4, 2) = 6 ways to choose the two positions in the same column. The remaining two tokens can be placed in any of the 6 remaining columns, so there are 6^2 = 36 possible positions for the remaining two tokens.

To account for both the horizontal and vertical sides having the same length, we multiply the number of possibilities together: 6 * 4 * 6 * 36 = 51,840.

The probability is then the ratio of the number of ways to form a non-degenerate rectangle to the total number of ways to choose positions: 51,840 / 18,874,368 = 5/1828.

Therefore, the value of a + b is 5 + 1828 = 1833.