**Bookstore Arrangement Problem**A bookstore manager wants to display 4 identical fantasy novels, 5 identical sci-fi novels, and 5 identical mystery novels on a shelf. How many different arrangements can be made?### a. Formula SelectionFor this example, which formula will we need to use?- **Combination:** \[ C_{r}^{n} = \frac{n!}{(n - r)! \cdot r!} \]- **Permutation Rule #2:** \[ \frac{n!}{n_{1}! \cdot n_{2}! \cdot \ldots \cdot n_{p}!} \]- **Permutation:** \[ P_{r}^{n} = \frac{n!}{(n - r)!} \]- **Fundamental Counting Rule:** \[ k_{1} \cdot k_{2} \cdot k_{3} \cdot \ldots \cdot k_{n} \]### b. Explanation for Formula SelectionWhy do we use this particular formula?- We are rearranging all the items that come from multiple groups (or categories), and within each group, there are identical items (repeats).### c. Calculation of ArrangementsHow many different arrangements can be made on the shelf? (Do the work on a separate piece of paper.)There are **_____** different ways to arrange the books on the shelf.**Note:** Recall that the permutation formula accounts for the total number of arrangements considering repeated items. For further assistance or clarification, please contact your instructor.

Here, we have n=4+5+5 total novels, out of which 4 are of type 1, 5 are of type 2, and 5 are of type…

A bookstore manager wants to display 4 identical fantasy novels, 5 Identical scl-fi novels, and 5 identical mystery novels on a shelf. How many different arrangements can be made? a. For this example, what formula will we need to use? n! O Combination: C, %3D - r)!•r! n! O Perumtation Rule #2: ... n! O Permutation: „P, %3D (n-r)! O Fundamental Counting Rule: k · k ks . kn b. Please explain how we know we are supposed to use that formula. O We are picking from multiple groups (or categories) and within each group have different choices. OWe are picking from one group multiple times and order matters. OWe are picking from one group multiple times and order does not matter. O We are rearranging all the items that come from multiple groups (or categories) and within each group there are identical items (repeats). c. How many different arrangements can be made on the shelf? (Do work on a separate piece of paper) There are different ways to arrange the books on the shelf.

A bookstore manager wants to display 4 identical fantasy novels, 5 Identical scl-fi novels, and 5 identical mystery novels on a shelf. How many different arrangements can be made? a. For this example, what formula will we need to use? n! O Combination: C, %3D - r)!•r! n! O Perumtation Rule #2: ... n! O Permutation: „P, %3D (n-r)! O Fundamental Counting Rule: k · k ks . kn b. Please explain how we know we are supposed to use that formula. O We are picking from multiple groups (or categories) and within each group have different choices. OWe are picking from one group multiple times and order matters. OWe are picking from one group multiple times and order does not matter. O We are rearranging all the items that come from multiple groups (or categories) and within each group there are identical items (repeats). c. How many different arrangements can be made on the shelf? (Do work on a separate piece of paper) There are different ways to arrange the books on the shelf.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

**Bookstore Arrangement Problem**

A bookstore manager wants to display 4 identical fantasy novels, 5 identical sci-fi novels, and 5 identical mystery novels on a shelf. How many different arrangements can be made?

### a. Formula Selection

For this example, which formula will we need to use?

- **Combination:**
\[
C_{r}^{n} = \frac{n!}{(n - r)! \cdot r!}
\]

- **Permutation Rule #2:**
\[
\frac{n!}{n_{1}! \cdot n_{2}! \cdot \ldots \cdot n_{p}!}
\]

- **Permutation:**
\[
P_{r}^{n} = \frac{n!}{(n - r)!}
\]

- **Fundamental Counting Rule:**
\[
k_{1} \cdot k_{2} \cdot k_{3} \cdot \ldots \cdot k_{n}
\]

### b. Explanation for Formula Selection

Why do we use this particular formula?

- We are rearranging all the items that come from multiple groups (or categories), and within each group, there are identical items (repeats).

### c. Calculation of Arrangements

How many different arrangements can be made on the shelf? (Do the work on a separate piece of paper.)

There are **_____** different ways to arrange the books on the shelf.

**Note:** Recall that the permutation formula accounts for the total number of arrangements considering repeated items.

For further assistance or clarification, please contact your instructor.

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