# Presents for all!

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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