A bookstore manager wants to select one novel from each category. There are 3 different fantasy novels, 2 different sci-fi novels, and 3 different mystery novels. How many different selections can be made? a. For this example, what formula will we need to use? n! O Perumtation Rule #2: rp! .... n! O Permutation: „P, (n-r)! n! O Combination: C, = %3D (n - r)! r! O Fundamental Counting Rule: k k2 k3. . kn .... b. Please explain how we know we are supposed to use that formula. O We are picking from one group multiple times and order does not matter. OWe are rearranging all the items that come from multiple groups (or categories) and within each group there are identical items (repeats). OWe 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. c. How many different selections can be made? (Do work on a separate piece of paper) There are different ways to arrange the books on the shelf.
A bookstore manager wants to select one novel from each category. There are 3 different fantasy novels, 2 different sci-fi novels, and 3 different mystery novels. How many different selections can be made? a. For this example, what formula will we need to use? n! O Perumtation Rule #2: rp! .... n! O Permutation: „P, (n-r)! n! O Combination: C, = %3D (n - r)! r! O Fundamental Counting Rule: k k2 k3. . kn .... b. Please explain how we know we are supposed to use that formula. O We are picking from one group multiple times and order does not matter. OWe are rearranging all the items that come from multiple groups (or categories) and within each group there are identical items (repeats). OWe 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. c. How many different selections can be made? (Do work on a separate piece of paper) There are different ways to arrange the books on the shelf.
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Question
![**Selecting Novels from Different Categories**
A bookstore manager wants to select one novel from each category. There are 3 different fantasy novels, 2 different sci-fi novels, and 3 different mystery novels. How many different selections can be made?
**a. Formula Selection**
For this example, what formula will we need to use?
- Permutation Rule #2:
\[
\frac{n!}{r_1! \cdot r_2! \cdot r_3! \cdot \ldots \cdot r_p!}
\]
- Permutation:
\[
n_P_r = \frac{n!}{(n-r)!}
\]
- Combination:
\[
n_C_r = \frac{n!}{(n-r)! \cdot r!}
\]
- Fundamental Counting Rule:
\[
k_1 \cdot k_2 \cdot k_3 \cdot \ldots \cdot k_n
\]
**b. Explanation of the Formula Usage**
Please explain how we know we are supposed to use that formula.
- We are picking from one group multiple times and order does not matter.
- We are rearranging all the items that come from multiple groups (or categories) and within each group there are identical items (repeats).
- We are picking from multiple groups (or categories) and within each group have different choices.
- We are picking from one group multiple times and order matters.
**c. Calculating Different Selections**
How many different selections can be made? (Do work on a separate piece of paper)
There are [blank] different ways to arrange the books on the shelf.
**Question Help:** [Message Instructor]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95e5e52d-4449-4f93-832b-400422add1f0%2F32c43794-c5d8-4a00-9e7f-ba082c2fa5bd%2Fnwekxb7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Selecting Novels from Different Categories**
A bookstore manager wants to select one novel from each category. There are 3 different fantasy novels, 2 different sci-fi novels, and 3 different mystery novels. How many different selections can be made?
**a. Formula Selection**
For this example, what formula will we need to use?
- Permutation Rule #2:
\[
\frac{n!}{r_1! \cdot r_2! \cdot r_3! \cdot \ldots \cdot r_p!}
\]
- Permutation:
\[
n_P_r = \frac{n!}{(n-r)!}
\]
- Combination:
\[
n_C_r = \frac{n!}{(n-r)! \cdot r!}
\]
- Fundamental Counting Rule:
\[
k_1 \cdot k_2 \cdot k_3 \cdot \ldots \cdot k_n
\]
**b. Explanation of the Formula Usage**
Please explain how we know we are supposed to use that formula.
- We are picking from one group multiple times and order does not matter.
- We are rearranging all the items that come from multiple groups (or categories) and within each group there are identical items (repeats).
- We are picking from multiple groups (or categories) and within each group have different choices.
- We are picking from one group multiple times and order matters.
**c. Calculating Different Selections**
How many different selections can be made? (Do work on a separate piece of paper)
There are [blank] different ways to arrange the books on the shelf.
**Question Help:** [Message Instructor]
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