# Missing Jigsaw Pieces

Discrete Mathematics Level 4

My little nephew is working on a jigsaw puzzle of 48 pieces ($$8 \times 6$$). It is an old puzzle, so it is not surprising that three pieces are missing.

What is more surprising, however, is that the three missing pieces are adjacent to each other: there is only one (big) hole in the puzzle!

"I bet the odds are, like, one in a million!" exclaims my nephew.

You know better than that, of course. Given that three pieces are missing from an $$8 \times 6$$ jigsaw puzzle, what is the probability $$p$$ that these pieces form a connected shape?

Give your answer in the form $$[1000000p]$$, i.e. multiply $$p$$ by one million and round to the nearest integer.

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