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Pretty tough combination problem Pretty tough combination problem

12-31-2021 , 07:53 AM
There is a contest where you have to select the winner of 17 football games. You cannot pick both teams from the same game obv.

There is a pool of 40 games to choose from but you must pick a team from 3 assigned games. (Call them games 1 2 3) The other 14 picks you can select from the remaining 37.

You must assign 3 of your 17 picks as key picks. These can be from one of the 3 mandatory games or one of your other 14.

To clarify...while you have to pick someone from games 1 2 3 the key picks can come from these or any of your other 14.

How many total unique entries are possible?
12-31-2021 , 08:30 AM
If I've understood correctly, it's this:

2^3 ways to pick from the 3 assigned games.

37C14 possible sets of 14 matches from the remaining 37.

2^14 ways to pick from your chosen 14 matches.

17C3 ways of assigning the 3 key picks from your 17.

Then multiply all these together:

= 544318295113728000


Last edited by jukofyork; 12-31-2021 at 08:39 AM. Reason: Added answer
12-31-2021 , 11:18 AM
Guess it was not that hard for you