SOLUTION: A club has 20 members. In how many different ways could they elect a president, a vice president and a three person newsletter committee?

Question 327147: A club has 20 members. In how many different ways could they elect a president, a vice president and a three person newsletter committee?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

That depends on whether the president and vice-president have to be different people (which would make sense in most scenarios) AND it would depend on whether the president and/or the vice-president were allowed to serve on the newsletter committee (which way that goes is not so obvious).

Let's assume that the 5 positions mentioned must be staffed with 5 different people. Then there are 20 ways to pick the President. For each of those 20 ways to pick the President, there are 19 ways to pick the Vice-President, and then 18 ways to pick the 1st committee member, and so on...

On the other hand, if the President and Vice-President have to be different people but are eligible to serve on the committee: Then there are 20 ways to pick the President. For each of those 20 ways to pick the President, there are 19 ways to pick the Vice-President, and then 20 ways to pick the 1st committee member, 19 ways to pick the 2nd committee member, and 18 ways to pick the 3rd committee member.

You get to do your own arithmetic in either case.

But what if the Prez and VP have to be different people, and the Prez can't serve on the committee, but the VP MUST be one of the three on the committee? I'll let you figure that one for yourself.

John

RELATED QUESTIONS
If the chamber of Commerce has 20 members, in how many ways can they elect a different... (answered by checkley77)

In how many ways can a twenty-person club choose three different people to be president,... (answered by stanbon)

A high school computer club has 15 members. In how many different ways can they choose a... (answered by stanbon)

In how many ways could a club of 18 members choose a president, vice president, and... (answered by josmiceli,ikleyn)

A 40-member club will elect a president and elect a vice president. How many possible... (answered by Theo)

how many ways are there to elect a president, vice president, secretary, and treasurer,... (answered by ikleyn)

How many ways can a club consisting of twenty-seven people elect a president, vice... (answered by lynnlo,MathTherapy)

In a club with 17 members, how many ways can the club elect a president and a treasurer? (answered by stanbon)

In a club with 17 members, how many ways can the club elect a president and a... (answered by jim_thompson5910)