There are \(4\) children awaiting their presents. \(7\) elves come one-by-one and each of them gives \(1\) present to exactly \(1\) child. Every elf chooses the child randomly.

The probability that each child receives at least one present is of the form \[\dfrac{A}{B}\] where \(A\) and \(B\) are co-prime positive integers. Find the value of \[B-A.\]

\(\textbf{Assumptions}\)

- Each elf has a different present.

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