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20.03.2020 • 
Mathematics

In a community chorus, 10 people are candidates for the board of directors. The board has 6 members: 4 officers (president, vice president, secretary, and treasurer) and 2 at-large members (who don’t have an office).

Part A: First, the four officers are chosen. In how many ways can 4 of the 10 candidates be chosen to be president, vice president, secretary, and treasurer? Is this a combination or a permutation?

Part B: Next, 2 of the remaining 6 candidates are chosen to be the at-large board members. In how many ways can they be chosen?

Part C: The chorus decides to choose the 2 at-large board members from the 6 remaining candidates randomly. What is a fair way to do this?

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