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Selecting Council Members The presidents, vice presidents, and secretary-treasurers from each of four classes are eligible for an all-school council. How many ways can four officers be chosen from these representatives? How many ways can they be chosen if the president must be selected from the sitting presidents, the vice president from the sitting vice presidents, the secretary from the sitting secretary-treasurers, and the treasurer from everybody who’s left?

Intro Stats / AP Statistics

Chapter 4

Probability and Counting Rules

Section 4

Counting Rules

Sampling and Data

Probability Topics

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Lectures

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A club has 25 members.…

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In a club with 15 members,…

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The College of Science Cou…

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03:06

Task Assignments How many …

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Electing Officers The 13 m…

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There are four classes each with the president, vice president and secretary treasurer on all school council with four officers is to be formed from these representatives. So in how many ways can you choose four officers from these representatives? Okay, so since each class has a precedent and there are four classes, then there would be four pressured dense among the representatives. Similarly, there would be four vice presidents and four secretary treasurer's. So for that question, you want to choose four officers from 12 representatives four plus four plus four, so that can be done in combination. 12. Taken four a number of ways. Now, if you have a calculator that could calculate combinations directly, then you can use that. Otherwise you'll need the combination rule, which basically says that combination and taken arms equal to n factorial over and minus R. Factorial times are editorial, which means this would be equal to 12 factorial over eight factorial. Thanks for factorial and you could use your calculator. This would be equal to 4 95 different ways for the next question from the four presidents. You want to choose one president for the Oil School Council from the four. Vice President. You want to choose one vice president from the four Secretary Treasurer? You want to choose one secretary in from whoever is left? You want to choose one Drescher her so we can use the fundamental counting room. In this case, there are 123 four slots to be filled. Four or four positions to be filled. President, Vice president, Secretary in treasurer. There are four choices for president. Four choices for vice president and four choices. Four. Secretary. No, since three off. The representatives have all already filled in positions and there are 12 of them. Then there would be nine left to fill in the position of treasurer. Invite the fundamental counting rule. We just need to multiply these to find the number of ways you can. You should calculator, and this should be equal to 576 weights of doing this

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