You are the manager of a softball league in the locality in which there are 5 local teams with 10 people each. The league has been arranged for parity so that each local team has 5 good players and 5 bad players. Another softball league located in another state wants to put together a regional all-star team for a tournament that would consist of 5 players from your league.
How many ways can the All-Star team can be assembled from the 50 players of the 5 teams, provided that no more than 2 members from any one team are selected?