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We have a pool of numbers 1 thru 22. We then draw four numbers. Once a number is drawn, it is out of the pool. We repeat the drawing until we have gone thru all the 7,315 combinations.

I used MATLAB function combntns(set,subset)

Now the hard part: Assume that you want to only keep combinations, where no more than 2 out of 4 numbers are the same.

What is the formula to find out how many valid combinations there are?

Here are the first few valid combinations: $(1,2,3,4):(1,2,5,6):(1,2,7,8):(1,2,9,10):(1,2,11,12):(1,2,13,14)...$

Thank you for the help - DJ

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    @Hardy: There is a pattern. There is nothing of the form $[1,9,y,z]$ because for any $y,z$ with $9 \lt y \lt z \le 22$ he already has at least one of $[1,x,9,y]$, $[1,x,9,z]$ or $[1,x,y,z]$ from earlier for some $x$ with $1 \lt x \lt 9$.2012-02-16

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