SOLUTION: Question: A club consists of 16 men and 19 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six

Question 483360: Question:
A club consists of 16 men and 19 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people?

Comment:
I think this is a matter of a permutation (the election of the positions) and a combination (the election of the committee), but I don't know how to solve them together. Can you help?

Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
Assuming the gender of each position is irrelevant; you have a total of 35 people.
You have 4 offices, and 6 committee members, so that's 10 people overall. So you're combining 35 people, ten at a time, which is:
35C10=35x34x33x32x31x30x29x28x27x26x25!/10x9x8x7x6x5x4x3x2x25!=183579396
different arrangements of officers and committee members..
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