**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

Combination Rule: The arrangement of r objects from n different objects is given by:

Answered: Evaluate the given expression and…

Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation). 22C2 22C2 =]

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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