Question

In the house of representatives of your state legislature there are 90 Democrats and 70 Republicans. By a random process, a Majority Leader and an Assistant Majority Leader will be selected from the Democrats and a Minority Leader and Assistant Minority Leader will be selected from the Republicans. How many permutations are there of these four leadership positions?

Name: Problem 33, Chapter 9: Schaum's Outline of Elements of Statistics I: Descriptive Statistics and Probability
Uploaded: 2020-07-20T19:12:10-08:00
Duration: 1 min 1 s
Channel: Kyler Gray
Description: In the house of representatives of your state legislature there are 90 Democrats and 70 Republicans. By a random process, a Majority Leader and an Assistant Majority Leader will be selected from the Democrats and a Minority Leader and Assistant Minority Leader will be selected from the Republicans. How many permutations are there of these four leadership positions?

    In the house of representatives of your state legislature there are 90 Democrats and 70 Republicans. By a random process, a Majority Leader and an Assistant Majority Leader will be selected from the Democrats and a Minority Leader and Assistant Minority Leader will be selected from the Republicans. How many permutations are there of these four leadership positions?

Schaum's Outline of Elements of Statistics I: Descriptive Statistics and Probability

Stephen Bernstein,… 1st Edition

Chapter 9, Problem 33

Instant Answer

Solved by Expert Kyler Gray

07/20/2020

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Since the positions are distinct, we need to consider permutations. Show more…

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In the house of representatives of your state legislature there are 90 Democrats and 70 Republicans. By a random process, a Majority Leader and an Assistant Majority Leader will be selected from the Democrats and a Minority Leader and Assistant Minority Leader will be selected from the Republicans. How many permutations are there of these four leadership positions?

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Key Concepts

Permutation Formula

The permutation formula, often expressed as P(n, r) = n! / (n - r)!, determines the number of ways to choose and arrange r objects from a set of n distinct objects. This is particularly relevant when the assignment of distinct positions or roles is involved, and the order of selection is important.

Permutation

A permutation is an arrangement of objects in a specific order. When assigning roles or positions where the order or specific assignment matters, permutations are used to count the number of possible arrangements without any repetition.

Fundamental Counting Principle

The fundamental counting principle states that if there are multiple independent tasks, the total number of outcomes is the product of the number of ways each task can occur. This principle allows us to calculate the total number of possibilities by multiplying the number of choices for each independent selection.

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