Question

The board of directors of the XYZ Corporation has 15 members. (a) How many different slates of four officers (a President, a Vice President, a Treasurer, and a Secretary) can be chosen? (b) A four-person committee needs to be selected to conduct a search for a new CEO. In how many ways can the search committee be selected?

Name: Problem 27, Chapter 16: Excursions in Modern Mathematics
Uploaded: 2020-08-03T20:58:45-08:00
Duration: 50 s
Channel: Heather Zimmers
Description: The board of directors of the XYZ Corporation has 15 members. (a) How many different slates of four officers (a President, a Vice President, a Treasurer, and a Secretary) can be chosen? (b) A four-person committee needs to be selected to conduct a search for a new CEO. In how many ways can the search committee be selected?

   The board of directors of the XYZ Corporation has 15 members.
(a) How many different slates of four officers (a President, a Vice President, a Treasurer, and a Secretary) can be chosen?
(b) A four-person committee needs to be selected to conduct a search for a new CEO. In how many ways can the search committee be selected?

Excursions in Modern Mathematics

Peter Tannenbaum 9th Edition

Chapter 16, Problem 27

Instant Answer

Solved by Expert Heather Zimmers

08/03/2020

Step 1

For the President position, we have 15 choices. For the Vice President position, we have 14 choices (since one person has already been chosen for the President position). For the Treasurer position, we have 13 choices (since two people have already been chosen Show more…

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The board of directors of the XYZ Corporation has 15 members. (a) How many different slates of four officers (a President, a Vice President, a Treasurer, and a Secretary) can be chosen? (b) A four-person committee needs to be selected to conduct a search for a new CEO. In how many ways can the search committee be selected?

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Key Concepts

Permutations

Permutations are used to count the number of ways to arrange a set of items where the order matters. This concept is crucial when assigning distinct roles or positions to members from a group, as each different ordering constitutes a unique permutation.

Combinations

Combinations count the number of ways to select items from a group where the order does not matter. This concept is important in situations such as forming committees or teams, where the arrangement of the selected members is irrelevant to the outcome.

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