### Problem 5: Election CombinationsA corporation has 10 members on its board of directors. In how many different ways can it elect a president, vice president, and treasurer?#### Concepts:**Circle one:** Counting Principle | **Permutation** | Combination#### Solution Setup:1. Determine if the order matters. Since the positions of president, vice president, and treasurer are distinctly different, the order of election is important. This calls for the use of permutations.2. Set Up: To find the number of permutations of selecting 3 positions from 10 members, use the formula for permutations $ P(n, r) $: $ P(n, r) = n! / (n-r)! $ where $ n = 10 $ and $ r = 3 $.3. Calculation: \[ P(10, 3) = \frac{10!}{(10-3)!} = \frac{10!}{7!} = 10 \times 9 \times 8 \]4. Compute the value: \[ 10 \times 9 \times 8 = 720 \]#### Answer: The number of different ways to elect a president, vice president, and treasurer is: **720**---This problem requires an understanding of basic permutation concepts, where the positions are distinct and the order of selection is crucial. The solution entails setting up the appropriate formula for permutations and calculating the final number of ways to elect the officials.

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Number of ways of arranging of doing something which has m ways of doing, further that m ways has n…

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5. A corporation has 10 members on its board of directors. In how many different ways can it elect a president, vice president, and treasurer? Circle one: Counting Principle Permutation Combination Set Up: Answer:

5. A corporation has 10 members on its board of directors. In how many different ways can it elect a president, vice president, and treasurer? Circle one: Counting Principle Permutation Combination Set Up: Answer:

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

### Problem 5: Election Combinations

A corporation has 10 members on its board of directors. In how many different ways can it elect a president, vice president, and treasurer?

#### Concepts:

**Circle one:** Counting Principle | **Permutation** | Combination

#### Solution Setup:

1. Determine if the order matters. Since the positions of president, vice president, and treasurer are distinctly different, the order of election is important. This calls for the use of permutations.

2. Set Up:
To find the number of permutations of selecting 3 positions from 10 members, use the formula for permutations $ P(n, r) $:
$ P(n, r) = n! / (n-r)! $
where $ n = 10 $ and $ r = 3 $.

3. Calculation:
\[
P(10, 3) = \frac{10!}{(10-3)!} = \frac{10!}{7!} = 10 \times 9 \times 8
\]
4. Compute the value:
\[
10 \times 9 \times 8 = 720
\]

#### Answer:
The number of different ways to elect a president, vice president, and treasurer is: **720**

---

This problem requires an understanding of basic permutation concepts, where the positions are distinct and the order of selection is crucial. The solution entails setting up the appropriate formula for permutations and calculating the final number of ways to elect the officials.

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