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hodyreva [135]
3 years ago
10

In the local frisbee league, teams have 7 members and each of the 4 teams takes turns hosting tournaments. At each tournament, e

ach team selects two members of that team to be on the tournament committee, except the host team, which selects three members. How many possible 9 member tournament committees are there?
Mathematics
1 answer:
mars1129 [50]3 years ago
8 0

There are 4 teams in total and each team has 7 members. One of the team will be the host team.

Tournament committee will be made from 3 members from the host team and 2 members from each of the three remaining teams. Selecting the members for tournament committee is a combinations problem. We have to select 3 members out 7 for host team and 2 members out of 7 from each of the remaining 3 teams.

So total number of possible 9 member tournament committees will be equal to:

7C3 \times 7C2 \times 7C2 \times 7C2\\ \\  = 324135

This is the case when a host team is fixed. Since any team can be the host team, there are 4 possible ways to select a host team. So the total number of possible 9 member tournament committee will be:

9 \times 324135\\ \\  =2917215

Therefore, there are 2917215 possible 9 member tournament committees

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