Hello sci, I'm struggling to solve a problem I came up with because of brainletness. In the free-to-play FPS Paladins there is a game mode called Siege. Siege is a 5 v 5 team game mode where players must capture a neutral capture point in the beginning of the round and spawn a playload. The team who spawns this payload must push it into the enemy's goal under two minutes (overtime exists but is irrelevant) while the enemy must defend their goal from the other team's payload.

Capturing the neutral payload counts as a point to the team who captured, as does successfully pushing it into the enemy goal. If a team successfully fends off a payload for two minutes (assuming no overtime) then the team who defended gets a point. A team needs 4 points to win a game with the condition that a team with 3/4 points will not get a defense point if they fail to capture the point. Based on these conditions I've been trying to solve how many possible games there are based on who caps, pushes and defends. The problem is that this seems much more complex than I realized and my small brain can't seem to find a good way to solve it through permutations with restrictions. Does anyone have any suggestions or solutions?