Find the following combinations ,C, (a) n= 8 andr=2. 8C2 (b) n=8 and r D1. BC1 (c) n=8 and r 6. 8C6 (d) n= 8 andr38. 8C8
Find the following combinations ,C, (a) n= 8 andr=2. 8C2 (b) n=8 and r D1. BC1 (c) n=8 and r 6. 8C6 (d) n= 8 andr38. 8C8
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
![**Find the following combinations \( nC_r \):**
**(a) \( n = 8 \) and \( r = 2 \)**
- \( 8C2 \) [Input box available to enter the answer]
**(b) \( n = 8 \) and \( r = 1 \)**
- \( 8C1 \) [Input box available to enter the answer]
**(c) \( n = 8 \) and \( r = 6 \)**
- \( 8C6 \) [Input box available to enter the answer]
**(d) \( n = 8 \) and \( r = 8 \)**
- \( 8C8 \) [Input box available to enter the answer]
---
### Explanation:
This section requires calculating combinations, denoted as \( nC_r \), which are used to determine the number of ways to choose \( r \) items from a total of \( n \) items without regard to the order of selection. The formula to calculate combinations is:
\[
nC_r = \frac{n!}{r!(n-r)!}
\]
Where \( n! \) (n factorial) is the product of all positive integers up to \( n \).
To solve each of the problems:
- **(a)** \( 8C2 \): Calculate how many ways to choose 2 items from 8.
- **(b)** \( 8C1 \): Calculate how many ways to choose 1 item from 8.
- **(c)** \( 8C6 \): Calculate how many ways to choose 6 items from 8.
- **(d)** \( 8C8 \): Calculate how many ways to choose all 8 items from 8.
By using the provided formula, the required values of combinations can be determined for each case.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadb882f8-f4be-49b7-a475-a003823b1c8d%2Fe96050a9-6d67-49e8-ac9a-bff4547fec67%2Fjolcl7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the following combinations \( nC_r \):**
**(a) \( n = 8 \) and \( r = 2 \)**
- \( 8C2 \) [Input box available to enter the answer]
**(b) \( n = 8 \) and \( r = 1 \)**
- \( 8C1 \) [Input box available to enter the answer]
**(c) \( n = 8 \) and \( r = 6 \)**
- \( 8C6 \) [Input box available to enter the answer]
**(d) \( n = 8 \) and \( r = 8 \)**
- \( 8C8 \) [Input box available to enter the answer]
---
### Explanation:
This section requires calculating combinations, denoted as \( nC_r \), which are used to determine the number of ways to choose \( r \) items from a total of \( n \) items without regard to the order of selection. The formula to calculate combinations is:
\[
nC_r = \frac{n!}{r!(n-r)!}
\]
Where \( n! \) (n factorial) is the product of all positive integers up to \( n \).
To solve each of the problems:
- **(a)** \( 8C2 \): Calculate how many ways to choose 2 items from 8.
- **(b)** \( 8C1 \): Calculate how many ways to choose 1 item from 8.
- **(c)** \( 8C6 \): Calculate how many ways to choose 6 items from 8.
- **(d)** \( 8C8 \): Calculate how many ways to choose all 8 items from 8.
By using the provided formula, the required values of combinations can be determined for each case.
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