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Playing Lotto (Posted on 2005-01-14) Difficulty: 4 of 5
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).

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(2): A simpler way of getting to solutionSteve Herman2005-01-18 17:17:10
Questionre: A simpler way of getting to solutionJay Schamel2005-01-18 11:32:06
re(2): Stirling Perhapsowl2005-01-16 21:06:36
SolutionA simpler way of getting to solutionSteve Herman2005-01-16 12:02:45
re(3): my solution....QUESTIONJay Schamel2005-01-15 21:34:56
Some Thoughtsre(2): my solution....QUESTIONAdy TZIDON2005-01-15 21:04:24
re: Stirling PerhapsCharlie2005-01-15 16:33:57
re: my solutionCharlie2005-01-15 15:45:14
Solutionmy solutionAdy TZIDON2005-01-15 07:40:44
re: Stirling PerhapsCharlie2005-01-15 04:58:53
SolutionStirling Perhapsowl2005-01-14 22:43:47
SolutionsolutionCharlie2005-01-14 19:35:20
Some ThoughtsthoughtsCharlie2005-01-14 19:00:49
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