Number of winning lines
I'm looking for a simple way to work out how many winning lines I have, in a 'UK Pools' type competition.
Here are the parameters;
select 1 of 3 outcomes - home win, draw, away win
for 1 selection on each match I pay 1 unit.
Each additional selection (i.e. for match 1, pick home AND draw) doubles the stake.
Winnings are paid on 12/12, 11/12 and 10/12 right.
This is what my current ticket looks like:
7 lines with 1x selected
3 lines with 2x selected
2 lines with 3x selected
This cost me 72 units.
I have every match right, so will win 1x the first prize.
I think I'll win 7x the 2nd prize..?
Cannot be sure of how many 3rd prizes.. which is 10 of 12 matches right!
There must be a formula i could use in these or similar circumstances, for example, if I had 1 match wrong with a 1x selection.
An interesting aside: One match was voided, which means all results are correct, I knew the match was not going to happen, but if I'd made a 2x selection for that match, I would have won 2x the first prize.
I think I have the answer, but not sure it's right. Hopefully someone will check and confirm please!
1 x 12/12
7 x 11/12
19 x 10/12
I am also hoping for a formula!