Let's say there are 12 games being played. One entry in the contest consists of picking the winners of any 7 of the 12 available games. I need all 7 to be correct to win. For the purposes of simplicity every team is evenly matched.

What would the odds be for selecting 7 winners from the 12 games being played with a single entry? Two entries? Three entries? How would I calculate this?

Now let's say I am submitting multiple entries. I am submitting every combination of picks for 4 games (2^4 = 16 combinations) to ensure at least one of the entries has all 4 picks correct. This would leave only 3 picks to chance. I would submit the same 3 picks with all 16 combinations. Therefore as long as my 3 guesses were correct, one of my 16 entries would have all 7 picks correct. How would I calculate these odds?

I hope this makes sense.

Thanks.