perplexus.info :: Probability : Playing Lotto

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.)

See The Solution Submitted by Federico Kereki

Rating: 4.0000 (4 votes)

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Puzzle Answer

Comment 14 of 14 |

C=#possible distinct combinations.

Then, the expected number of DIFFERENT combinations that will be chosen, if N persons play is C(1-(1-1/C)^N)..

Edited on September 30, 2023, 9:21 am

Posted by K Sengupta on 2023-09-30 09:20:43

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