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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