**Combinatorics Task: Evaluating Combinations and Permutations** This exercise involves evaluating a combination and a permutation: 1. **Evaluate \( \binom{11}{3} \):** The expression \( \binom{11}{3} \) represents a combination, specifically selecting 3 objects from a set of 11 without regard to the order of selection. The result is a specific value which needs to be calculated. 2. **Evaluate \( _{7}P_{4} \):** The expression \( _{7}P_{4} \) represents a permutation, specifically arranging 4 objects from a set of 7 in a particular order. The result is a specific value which needs to be calculated. **Inputs:** - The fields are represented as boxes for inputting the calculated values of the combination and permutation. **Additional Interface Details:** - There are three icons below the input fields: an "X" for closing or canceling the input, a circular arrow for resetting the input, and a question mark, likely for help or additional information on how to perform the calculations. **Instructions for Completion:** - Calculate each value using the formula for combinations and permutations. - Input the results in the respective boxes.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Combinatorics Task: Evaluating Combinations and Permutations**

This exercise involves evaluating a combination and a permutation:

1. **Evaluate \( \binom{11}{3} \):**

   The expression \( \binom{11}{3} \) represents a combination, specifically selecting 3 objects from a set of 11 without regard to the order of selection. The result is a specific value which needs to be calculated.

2. **Evaluate \( _{7}P_{4} \):**

   The expression \( _{7}P_{4} \) represents a permutation, specifically arranging 4 objects from a set of 7 in a particular order. The result is a specific value which needs to be calculated.

**Inputs:**

- The fields are represented as boxes for inputting the calculated values of the combination and permutation.

**Additional Interface Details:**

- There are three icons below the input fields: an "X" for closing or canceling the input, a circular arrow for resetting the input, and a question mark, likely for help or additional information on how to perform the calculations.

**Instructions for Completion:**

- Calculate each value using the formula for combinations and permutations.
- Input the results in the respective boxes.
Transcribed Image Text:**Combinatorics Task: Evaluating Combinations and Permutations** This exercise involves evaluating a combination and a permutation: 1. **Evaluate \( \binom{11}{3} \):** The expression \( \binom{11}{3} \) represents a combination, specifically selecting 3 objects from a set of 11 without regard to the order of selection. The result is a specific value which needs to be calculated. 2. **Evaluate \( _{7}P_{4} \):** The expression \( _{7}P_{4} \) represents a permutation, specifically arranging 4 objects from a set of 7 in a particular order. The result is a specific value which needs to be calculated. **Inputs:** - The fields are represented as boxes for inputting the calculated values of the combination and permutation. **Additional Interface Details:** - There are three icons below the input fields: an "X" for closing or canceling the input, a circular arrow for resetting the input, and a question mark, likely for help or additional information on how to perform the calculations. **Instructions for Completion:** - Calculate each value using the formula for combinations and permutations. - Input the results in the respective boxes.
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P47

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