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Printjmc
counting and probability senior
Problem
My school's Physics Club has 22 members. It needs to select 3 officers: chairman, vice-chairman, and sergeant-at-arms. Each person can hold at most one office. Two of the members, Penelope and Quentin, will only be officers if the other one is also an officer. (In other words, either both Penelope and Quentin are officers, or neither are.) In how many ways can the club choose its officers?
Solution
If both Penelope and Quentin are not officers, then there are 20 choices for chairman, 19 choices for vice-chairman, and 18 choices for sergeant-at-arms. There are ways in this case.
If both are officers, Penelope can take one of the 3 positions, Quentin can take one of the 2 remaining positions, and one of the 20 remaining members can take the third position. There are ways in this case.
The answer is
If both are officers, Penelope can take one of the 3 positions, Quentin can take one of the 2 remaining positions, and one of the 20 remaining members can take the third position. There are ways in this case.
The answer is
Final answer
6960