Date: 5/16/96 at 18:47:34 From: Chad Dellinger Subject: Permutations We am trying to determine the number of unique permutations of a lottery where you pick 6 numbers out of 49, with numbers not allowed to repeat. Also, we are having some trouble determining the odds of picking the winning set randomly. Finally, we are having a heated discussion on how buying a large number (unrealistically large), say 5,000,000 lotto tickets, would affect your odds of picking the winning numbers. Given a lotto that had odds of winning of say 1:7,000,000, would buying 7,000,000 tickets increase your odds to 1:1? Thanks for your help. Chad
Date: 6/14/96 at 19:7:49 From: Doctor Anthony Subject: Re: Permutations The number of possible combinations of 6 numbers selected from 49 (without repetition) is 49_C_6 = 13,983,816 So probability of a correct set is 1/(49_C_6) If you bought 5 million tickets, then you would have 5 million chances out of 14 million odds of having the winning ticket. To give yourself a probability of 1 of having a winning ticket, you would have to buy ~14 million. Since many others might have the winning numbers as well, you could end up sharing the prize, and so reduce very considerably what you earn. Against that, you would also be winning all the possible lesser prizes of having 5 right numbers, 4 right numbers, and so on with other tickets that you had bought. Buying a large number of tickets might change your expectation marginally if the lesser prizes were generous, but your expectation will always be highly negative. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.