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A standard 52 card deck is being used in an exciting experiment! A card is drawn randomly from the deck, its information is recorded, then

A standard 52 card deck is being used in an exciting experiment! A card is drawn randomly from the deck, its information is recorded, then the card is returned to the deck and it is thoroughly shuffled.

Suppose we repeat this experiment 8 times. Determine the conditional probability that we draw exactly 5 diamonds and exactly 1 club if we know that we drew exactly 2 black cards.

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