Generating Possible Lottery Outcomes

Date: 3/29/96 at 19:52:17
From: Anonymous
Subject: Lottery

What math rule would I need to follow if I wanted to generate all
possible combinations in a 50 number draw 6 lottery? (15,890,700).
I have a programmer friend who is willing to write the program but
needs a rule to follow.  If you don't have time for this problem, will
you recommend a source where I can get the answer?

Thanks
Stan

Date: 6/13/96 at 21:17:23
From: Doctor Ethan
Subject: Re: Math Rule

Hey Stan,

I am assuming that in this lottery 2 3 4 and 3 2 4 would be the same
thing - i.e. that order doesn't matter.

I also am assuming that a number cannot be repeated.

Otherwise, the number 15,890,700 doesn't make sense.

Given that, here is my idea.  I will leave it to you to check it.

start with 

1,2,3,4,5 -> 1,2,3,4,6 ->1,2,3,4,7-> ... 1,2,3,4,50
1,2,3,5,6 -> 1,2,3,5,7 ->1,2,3,5,8-> ... 1,2,3,5,50
.
.
.
1,2,4,5,6->
.
.
.
.
.
1,3,4,5,6 ->

Hope that helps.  

By the way I heard a good joke about the Lottery.

Lottery: Definition: A tax for the mathematically incompetent.

-Doctor Ethan,  The Math Forum