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 Playing Lotto (Posted on 2005-01-14)
A Lotto bet is picking 6 numbers out of 49 -- if you pick the correct combination, you get the jackpot!

If N persons play, there will be many repeats, since it's highly probable that some combinations will be chosen by two persons or more. (This is known as the "birthday paradox".)

What's the expected number of DIFFERENT combinations that will be chosen, if N persons play? (Assume these persons pick their combinations totally randomly.)

 Submitted by Federico Kereki Rating: 3.7500 (4 votes) Solution: (Hide) If there are C possible distinct combinations, the odds of nobody winning are (1-1/C)^N, so the odds of somebody winning are 1-(1-1/C)^N, which represents the percentage of played distinct combinations, so the answer is C(1-(1-1/C)^N).

 Subject Author Date re(2): A simpler way of getting to solution Steve Herman 2005-01-18 17:17:10 re: A simpler way of getting to solution Jay Schamel 2005-01-18 11:32:06 re(2): Stirling Perhaps owl 2005-01-16 21:06:36 A simpler way of getting to solution Steve Herman 2005-01-16 12:02:45 re(3): my solution....QUESTION Jay Schamel 2005-01-15 21:34:56 re(2): my solution....QUESTION Ady TZIDON 2005-01-15 21:04:24 re: Stirling Perhaps Charlie 2005-01-15 16:33:57 re: my solution Charlie 2005-01-15 15:45:14 my solution Ady TZIDON 2005-01-15 07:40:44 re: Stirling Perhaps Charlie 2005-01-15 04:58:53 Stirling Perhaps owl 2005-01-14 22:43:47 solution Charlie 2005-01-14 19:35:20 thoughts Charlie 2005-01-14 19:00:49

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