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There are 5*54 ways to get 4 of 5 numbers to match (5 ways to choose which number doesn't match times 54 wrong numbers it could be if it doesn't match). So there are 270 tickets that could match exactly 4 out of 5 numbers, not counting the one that matches all 5. Compare that with the overall number of tickets available, which is C(59,5) or 59*58*57*56*55/120, and you get odds of about 1:18541.

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