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There are 50 distinct numbers in a box, 1 to 50. Bob writes down 8 distinct numbers beforehand from the range of 1 to 50.

There are 50 distinct numbers in a box, 1 to 50. Bob writes down 8 distinct numbers beforehand from the range of 1 to 50. You randomly pick 12 numbers from the box, without replacement. What is the probability that

(a) none of the 8 numbers that Bob wrote down was picked?

(b) exactly 5 of the numbers that Bob wrote down were picked?

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