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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.)
Question re: A simpler way of getting to solution | Comment 12 of 13 |
(In reply to A simpler way of getting to solution by Steve Herman)

I'm having a little trouble seeing why the probability that nobody wins is 1-(D/C)  (which is the same as saying the Expected # of distinct picks is equal to the probability of someone winning * C).  Could you explain your reasoning?  Thanks!
  Posted by Jay Schamel on 2005-01-18 11:32:06

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