Given an eight-person committee, how many ways are there to choose the officer positions (chair person, vice-chairperson, and secretary) if a specific member of the committee (Angie) is either the vice-chairperson or she is not an officer?
There are a total of P(8, 3) = 8 * 7 * 6 = 336 ways to choose the officers without the last condition. However, given the condition the question has me stumped. Any suggestions?
Hello, battery88!
We must "talk" our way through this.
Given an eight-person committee, how many ways are there to choose the officer positions
(chair person, vice-chairperson, and secretary) if a specific member of the committee (Angie)
is either the vice-chairperson or she is not an officer?
It seems that Angie wants to be Vice-chair or nothing at all.
Very well, consider the two cases.
(1) Angie is Vice-chairman.
Then the other two offices (Chair, Secretary) can be filled in: ways.
(2) Angie is not Vice-chairman. .(Angie is "out of the running".)
Then the three offices can be filled by the other seven members: ways.
Answer: . ways.