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In: Statistics and Probability

How many ways are there to select a committee of 17 politicians chosen from a room...

How many ways are there to select a committee of 17 politicians chosen from a room full of indistinguishable Democrats, indistinguishable Republicans, and indistinguishable Independents if every party must have at least two members on the committee? If, in addition, no group may have a majority of the committee members?

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Answer:

Given that:

To select a committee of 17 politicians chosen from a room full of indistinguishable Democrats, indistiguishable Republicans, and indistinguishable independent if every party must have at least two members on the committee ,if in addition ,no group may have a majority of the committee.

In order to have majority , the number of member is one party must be greater than the number of member in other party.

This means that one of the party must have atleast 9 members.

a) Every party must have atleast two members on the committee

  

  

b) No group may have a majority of the committee members.

Since ,both parties cannot have 9 members thus on order to compute the committee number in a way that no group may have a majority of the committee members

  

  

  

orchestra answered 2 years ago
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