#16 Compute P99 #18 Compute C83
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Problem 16:** Compute \( P_{9,9} \)
**Problem 18:** Compute \( C_{8,3} \)
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### Educational Guide
#### Understanding \( P_{9,9} \) and \( C_{8,3} \)
The problems above require the computation of permutations and combinations, which are fundamental concepts in combinatorics.
**1. Permutation \( P_{9,9} \):**
- **Concept:** Permutations refer to the arrangement of objects in a specific order. The notation \( P_{n,r} \) represents the number of ways to arrange \( r \) elements out of \( n \) total elements.
- **Example for \( P_{9,9} \):** Since \( P_{9,9} \) involves arranging all 9 elements, the calculation is:
\[
P_{9,9} = 9!
\]
Where \( 9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \).
**2. Combination \( C_{8,3} \):**
- **Concept:** Combinations refer to the selection of objects where the order does not matter. The notation \( C_{n,r} \) indicates the number of ways to choose \( r \) elements from \( n \) elements.
- **Example for \( C_{8,3} \):** The formula to calculate combinations is:
\[
C_{8,3} = \frac{8!}{3!(8-3)!}
\]
Where \( 8! \) is the factorial of 8, and \( 3! \) and \( 5! \) are the factorials of 3 and 5, respectively.
These computations illustrate the difference between arranging (permutations) and selecting (combinations) elements from a set, critical for solving problems in probability and statistics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef9e1184-d530-448b-8cef-1f47d4bcc9be%2F3c1a628b-bec5-4785-a791-ce796b8b46cb%2Ffikqafk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 16:** Compute \( P_{9,9} \)
**Problem 18:** Compute \( C_{8,3} \)
---
### Educational Guide
#### Understanding \( P_{9,9} \) and \( C_{8,3} \)
The problems above require the computation of permutations and combinations, which are fundamental concepts in combinatorics.
**1. Permutation \( P_{9,9} \):**
- **Concept:** Permutations refer to the arrangement of objects in a specific order. The notation \( P_{n,r} \) represents the number of ways to arrange \( r \) elements out of \( n \) total elements.
- **Example for \( P_{9,9} \):** Since \( P_{9,9} \) involves arranging all 9 elements, the calculation is:
\[
P_{9,9} = 9!
\]
Where \( 9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \).
**2. Combination \( C_{8,3} \):**
- **Concept:** Combinations refer to the selection of objects where the order does not matter. The notation \( C_{n,r} \) indicates the number of ways to choose \( r \) elements from \( n \) elements.
- **Example for \( C_{8,3} \):** The formula to calculate combinations is:
\[
C_{8,3} = \frac{8!}{3!(8-3)!}
\]
Where \( 8! \) is the factorial of 8, and \( 3! \) and \( 5! \) are the factorials of 3 and 5, respectively.
These computations illustrate the difference between arranging (permutations) and selecting (combinations) elements from a set, critical for solving problems in probability and statistics.
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