/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 42 A corporation has seven members ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 42

A corporation has seven members on its board of directors. In how many different ways can it elect a president, vicepresident, secretary, and treasurer?

Short Answer

Expert verified
There are 840 different ways to elect a president, vice president, secretary, and treasurer from a seven-member board of directors.

Step by step solution

01

Understand the problem

First identify how many options are available for each position. Initially there are 7 directors available to be chosen for the first position.
02

Calculate the first permutation

Since there are 7 equally likely candidates for president, there are 7 ways to elect the president.
03

Calculate the second permutation

Once a president has been elected, there are now 6 directors remaining. Thus, the number of possible ways to elect the vice-president is 6.
04

Calculate the third permutation

Once the president and vice-president positions have been filled, there are now 5 directors remaining. Thus, there are 5 ways to elect the secretary.
05

Calculate the fourth permutation

With the president, vice-president, and secretary decided, only 4 directors remain to be the treasurer. Thus, there are 4 ways to elect the treasurer.
06

Calculate the total permutations

To find the total number of permutations, we multiply the number of ways to elect the president, vice-president, secretary, and treasurer (from Steps 2 to 5). So, the total number of permutations is \(7 * 6 * 5 * 4 = 840\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Involve computing expected values in games of chance. Another option in a roulette game (see Example 6 on page 753 ) is to bet \(\$ 1\) on red. (There are 18 red compartments, 18 black compartments, and 2 compartments that are neither red nor black.) If the ball lands on red, you get to keep the \(\$ 1\) that you paid to play the game and you are awarded \(\$ 1\). If the ball lands elsewhere, you are awarded nothing and the \(\$ 1\) that you bet is collected. Find the expected value for playing roulette if you bet \(\$ 1\) on red. Describe what this number means.

A social security number contains nine digits, such as 074-66-7795. How many different social security numbers can be formed?

We return to our box of chocolates. There are 30 chocolates in the box, all identically shaped. Five are filled with coconut, 10 with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting two caramel-filled chocolates in a row.

How many four-digit odd numbers are there? Assume that the digit on the left cannot be 0 .

Evaluate each factorial expression. \(\frac{17 !}{9 !}\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.