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A radio station runs a promotion at an auto show with a money box with 11 $50 tickets, 13 $25 tickets, and 12 $5 tickets.

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A radio station runs a promotion at an auto show with a money box with 11 $50 tickets, 13 $25 tickets, and 12 $5 tickets. The box contains an additional 20 "dummy" tickets with no value. Find the probability that three $50 prizes are chosen. The probability that three $50 prizes are chosen is (Round to five decimal places as needed.)

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