Sharing Chocolate Bars

Diamond and Cookie are sharing some chocolate. They have two bars, one milk and one dark. The dark chocolate bar has 35 rectangular sections, and 5 across the top. The milk chocolate bar has 32 square sections, and 4 across the top.

They each pick a random piece from either the dark or milk bar. What is the probability that Diamond gets a corner piece from the milk bar and then Cookie gets a non-corner edge piece from the dark bar?

Assume that each bar has 4 corners, and that it is random whether they pick the milk or dark bar.

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