Someone asked me how to do this and since I'm no math wiz I started to reply to him that it was too complicated for my math challenged mind but as I was typing I couldn't help but think it through and I think I actually figured it out. I was hoping someone with math chops could double check me and make sure I've got this right.
First thing we need to do is figure out total number of RB and WR combinations right?
n Choose r or C(n,r) So C(RB,2) C(WR,3).
Then we need to get the total number of flex players. So Flex = ((RB+WR+TE) -6) We have to subtract 6 from the total because we will already be using 6 of those players from the RB, WR, TE pool.
Now we just multiply those with the totals from the other positions together to get the total number of possible lineups correct?
Total number of possible lineups = QB * C(RB,2) * C(WR,3) * TE * ((RB+WR+TE) -6) * DST
So if we have a player pool with 5 players at each position it would be
5 * (C(5,2)=10) * (C(5,3)=10) * 5 * (((5+5+5)-6)=9) * 5 = 112,500 possible lineup combinations
5 * 10 * 10 * 5 * 9 * 5 = 112,500
I put this into a quick, simple google spreadsheet using the COMBIN(n,r) function to get the RB/WR sets and it seems to be working fine and seems to be correct but I wanted someone who actually has a clue look it over and make sure I'm not missing something.