So a soccer team is creating a team of 11, out of 22 players. There are 4 positions, which a certain number of people want: 2 wants to play keeper, 8 wants to play defense, 8 wants to play middle field and 4 wants to play offense. The number of spots available per position is: 1 for keeper, 4 for defense, 4 for middle field and 2 for offense.
The conditions are these: Mary and Sue only wants to join the team if both get the middle field position. Francis only wants to join the team if the Harold doesn't get the middle field position. Lastly one of the candidates for the offense position, Chris, rather wants to join the middle field position.
So there are a total of 9 players who wants the middle field position.
The question is: Assuming that the coach picks a team according to everyone's preferences, will Chris have a better chance of joining the team if he switches his preferences to the middle field, from offense?
I've tried a number of ways to attack this problem, I figured the amount of combinations for one player to join the middle field is 56 out of 126 possible. I'm struggling with how to find the amount of combinations for Mary and Sue.
I don't necessarily need the total answer, just a hint or a reference to a rule would be of much help.