Question

A corporation has ten members on its board of directors. In how many different ways can it elect a president, vice president, secretary, and treasurer? For a segment of a radio show, a disc jockey can play 7 songs. If there are 13 songs to select from, in how many ways can the program for this segment be arranged?

Name: Problem 43, Chapter 8: College Algebra
Uploaded: 2023-03-28T13:44:06-08:00
Duration: 1 min 39 s
Channel: Lauren Shelton
Description: A corporation has ten members on its board of directors. In how many different ways can it elect a president, vice president, secretary, and treasurer? For a segment of a radio show, a disc jockey can play 7 songs. If there are 13 songs to select from, in how many ways can the program for this segment be arranged?

   A corporation has ten members on its board of directors. In how many different ways can it elect a president, vice president, secretary, and treasurer?
For a segment of a radio show, a disc jockey can play 7 songs. If there are 13 songs to select from, in how many ways can the program for this segment be arranged?

College Algebra

Robert Blitzer 7th Edition

Chapter 8, Problem 43

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Solved by Expert Lauren Shelton

03/28/2023

Step 1

The order of selection matters here because each position is unique. This is a permutation problem. The formula for permutation is given by: \[ P(n, r) = \frac{n!}{(n-r)!} \] where \( n \) is the total number of items, \( r \) is the number of items to choose, Show more…

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A corporation has ten members on its board of directors. In how many different ways can it elect a president, vice president, secretary, and treasurer? For a segment of a radio show, a disc jockey can play 7 songs. If there are 13 songs to select from, in how many ways can the program for this segment be arranged?

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Key Concepts

Permutation

Permutation is a counting technique used when the order of selection matters. It calculates the number of ways to arrange or assign roles, positions, or items from a larger set, typically using the formula P(n, k) = n!/(n-k)! where n is the total number and k is the number of positions or items being arranged.

Multiplication Principle

The multiplication principle is a fundamental counting concept that states if one event can occur in m ways and a second event can occur independently in n ways, then the total number of ways both events can occur in sequence is m multiplied by n. This principle extends to multiple sequential decisions or selections, and is often used in problems involving ordered assignments or arrangements.

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