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.)

(In reply to re: Stirling Perhaps by Charlie)

I have little doubt that my sum and your neat formula are one and the same. There are an amazing number of nice identities floating around in these problems. And attacking the problem from different angles (as we did) generate the identities much faster than jumping through algebra hoops. Shine! 

Posted by owl on 2005-01-16 21:06:36