Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation). 23 C3
Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation). 23 C3
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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Question
![**Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation).**
\[ ^{23}C_3 \]
This expression represents the combination formula, which calculates the number of ways to choose 3 items from a total of 23 items without regard to the order of selection. The formula for combinations is given by:
\[ ^nC_r = \frac{n!}{r!(n-r)!} \]
Here, \( n = 23 \) and \( r = 3 \).
**Calculation:**
\[ ^{23}C_3 = \frac{23!}{3!(23-3)!} = \frac{23 \times 22 \times 21}{3 \times 2 \times 1} = 1771 \]
So, the result is 1,771.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31448140-8fa1-467a-b5ce-16527eeb2607%2Fe3d3e9f9-4805-466a-99d3-d775143f6355%2F5xvlwlf_processed.png&w=3840&q=75)
Transcribed Image Text:**Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation).**
\[ ^{23}C_3 \]
This expression represents the combination formula, which calculates the number of ways to choose 3 items from a total of 23 items without regard to the order of selection. The formula for combinations is given by:
\[ ^nC_r = \frac{n!}{r!(n-r)!} \]
Here, \( n = 23 \) and \( r = 3 \).
**Calculation:**
\[ ^{23}C_3 = \frac{23!}{3!(23-3)!} = \frac{23 \times 22 \times 21}{3 \times 2 \times 1} = 1771 \]
So, the result is 1,771.
![**Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation).**
\[ ^{53}P_2 \]
**Explanation:**
The expression \( ^{53}P_2 \) represents a permutation, which is used to find the number of ways to arrange 2 items out of a total of 53 items. The formula for permutations is given by:
\[ ^nP_r = \frac{n!}{(n-r)!} \]
In this case, \( n = 53 \) and \( r = 2 \). Plugging these values into the formula, we get:
\[ ^{53}P_2 = \frac{53!}{(53-2)!} = \frac{53!}{51!} \]
This simplifies to:
\[ 53 \times 52 = 2756 \]
So, the result is 2756.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31448140-8fa1-467a-b5ce-16527eeb2607%2Fe3d3e9f9-4805-466a-99d3-d775143f6355%2F34rie9a_processed.png&w=3840&q=75)
Transcribed Image Text:**Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation).**
\[ ^{53}P_2 \]
**Explanation:**
The expression \( ^{53}P_2 \) represents a permutation, which is used to find the number of ways to arrange 2 items out of a total of 53 items. The formula for permutations is given by:
\[ ^nP_r = \frac{n!}{(n-r)!} \]
In this case, \( n = 53 \) and \( r = 2 \). Plugging these values into the formula, we get:
\[ ^{53}P_2 = \frac{53!}{(53-2)!} = \frac{53!}{51!} \]
This simplifies to:
\[ 53 \times 52 = 2756 \]
So, the result is 2756.
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