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Hypergeometric/Binomial Probability Distribution

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?

Solution Preview

There are five teams each having 5 good players. We can choose 5 star players in number of ways.
Since we cannot choose more than 2 players from each team, we can choose 2+2+1 or 2+1+1+1 or 1+1+1+1+1
First we calculate number of ways in which we can choose 2 players each from two teams and 1 player from the remianing three teams.
Process is like ...

Solution Summary

This solution shows step-by-step calculations to determine the combination/permutation requirements to assemble the All-Start team with specific conditions.