Mind your rows and columns .....

On a standard \(8\) by \(8\) chessboard, \(k\) pawns are randomly placed in different squares, (with \(1 \le k \le 64\)). Let \(p(k)\) be the probability that, with \(k\) pawns being so placed, no two pawns lie in the same row or column as each other.

If \(p(3) + p(4) + p(5) + p(6) = \dfrac{a}{b}\), where \(a\) and \(b\) are positive coprime integers, then find \(b - a\).

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