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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.)

See The Solution Submitted by Federico Kereki    
Rating: 3.7500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Stirling Perhaps | Comment 7 of 13 |
(In reply to Stirling Perhaps by owl)

BTW, regarding "Taking Charlie's suggestion, using 10 instead of C[49,6], the formula gives 8.78423 for 20 people and 9.99973 for 100 people.", after my typo was corrected, if you substitute 10, it becomes 10*(1-(9/10)^N), and the numbers agree with these two quoted.
  Posted by Charlie on 2005-01-15 16:33:57

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