A group of 15 activists (7 Democrats, 6 Republicans and 2 Independents) want to form a...
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A group of 15 activists (7 Democrats, 6 Republicans and 2 Independents) want to form a committee so that they can change the world. The committee is to have 6 members on it, with 2 representatives from each party. After the committee has been formed, they will appoint a Grand Poobah, a semi-Poobah and a Gofur (these jobs are very different). How many different committees can be formed?
Homework Answers
Total number of members = 6 (2 representatives from each party)
Number of ways of selecting 2 Democrats = 7C2 = 21
Number of ways of selecting 2 republicans = 6C2 = 15
Number of ways of selecting 2 Independents = 2C2 = 1
Now that the committee is formed, we need to appoint a Grand Poobah, semi-Poobah and a Gofur.
A Grand Poobah can be appointed from 6 members in 6C1 ways
A Poobah can be appointed from the rest of the 5 members in 5C1
ways
A Gofur can be appointed in 4C1 ways.
Hence, total different committees which can be formed is: 21 x 15 x 1 x 6 x 5 x 4 = 37,800
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