Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation). 22C2 22C2 =]
Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation). 22C2 22C2 =]
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
![**Combinatorics and Binomial Coefficients**
**Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation):**
\[ {}^{22}C_{2} \]
**\[ {}^{22}C_{2} = \]**
---
**Instructions:**
Enter your answer in the answer box and then click "Check Answer."
---
**Detailed Steps:**
1. **Understanding the Notation:**
- The expression \({}^{22}C_{2}\) represents a binomial coefficient, also known as a combination.
- The notation \({}^{n}C_{r}\) or \(C(n,r)\) denotes the number of ways to choose \(r\) elements from a set of \(n\) elements without regard to the order of selection.
2. **Formula:**
\[
{}^{n}C_{r} = \frac{n!}{r!(n-r)!}
\]
3. **Applying the Formula:**
- For \({}^{22}C_{2}\):
\[
{}^{22}C_{2} = \frac{22!}{2!(22-2)!}
\]
\[
= \frac{22!}{2! \cdot 20!}
\]
4. **Simplification:**
- Expand the factorials:
\[
= \frac{22 \times 21 \times 20!}{2 \times 1 \times 20!}
\]
- Cancel the \(20!\) from numerator and denominator:
\[
= \frac{22 \times 21}{2 \times 1}
\]
- Simplify:
\[
= \frac{462}{2}
\]
\[
= 231
\]
5. **Final Result:**
- Therefore, \({}^{22}C_{2} = 231\)
---
**User Interface:**
- **Answer Box:** A text box is provided for inputting your evaluated result.
- **Buttons:**
- "Check Answer": Submits the entered answer for verification.
- "Clear All": Clears all inputs in the answer box.
- "OK": Confirms and proceeds.
Graphically, there are tabs on the left-hand side of the interface indicating various sections such](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadf5dfe6-7ed2-45f8-b250-c60bd8f0748b%2F3e6892b4-0910-4fae-8898-ae7a88faeb6e%2F68z2dgd_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:**Combinatorics and Binomial Coefficients**
**Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation):**
\[ {}^{22}C_{2} \]
**\[ {}^{22}C_{2} = \]**
---
**Instructions:**
Enter your answer in the answer box and then click "Check Answer."
---
**Detailed Steps:**
1. **Understanding the Notation:**
- The expression \({}^{22}C_{2}\) represents a binomial coefficient, also known as a combination.
- The notation \({}^{n}C_{r}\) or \(C(n,r)\) denotes the number of ways to choose \(r\) elements from a set of \(n\) elements without regard to the order of selection.
2. **Formula:**
\[
{}^{n}C_{r} = \frac{n!}{r!(n-r)!}
\]
3. **Applying the Formula:**
- For \({}^{22}C_{2}\):
\[
{}^{22}C_{2} = \frac{22!}{2!(22-2)!}
\]
\[
= \frac{22!}{2! \cdot 20!}
\]
4. **Simplification:**
- Expand the factorials:
\[
= \frac{22 \times 21 \times 20!}{2 \times 1 \times 20!}
\]
- Cancel the \(20!\) from numerator and denominator:
\[
= \frac{22 \times 21}{2 \times 1}
\]
- Simplify:
\[
= \frac{462}{2}
\]
\[
= 231
\]
5. **Final Result:**
- Therefore, \({}^{22}C_{2} = 231\)
---
**User Interface:**
- **Answer Box:** A text box is provided for inputting your evaluated result.
- **Buttons:**
- "Check Answer": Submits the entered answer for verification.
- "Clear All": Clears all inputs in the answer box.
- "OK": Confirms and proceeds.
Graphically, there are tabs on the left-hand side of the interface indicating various sections such
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