Lottery Permutations

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/