# 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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