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What is the probability of selecting a permutation in which 2 precedes 1? Multiple Choice O 1

What is the probability of selecting a permutation in which 2 precedes 1? Multiple Choice O 1

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Educational Content: Probability in Permutations** --- **Title: Understanding Probability in Permutations** **Section 1: Problem Overview** **Question:** What is the probability of selecting a permutation in which 2 precedes 1? **Context:** Consider the set of all permutations of \( \{1, 2, \ldots, n\} \) where \( n \geq 4 \). This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. **Section 2: Answer Choices** **Multiple Choice Options:** - \( \frac{1}{4} \) - \( 1 \) - \( \frac{1}{2} \) - \( \frac{1}{3} \) **Section 3: Explanation of Concepts** Permutations of a set refer to all possible arrangements of its elements. Here, we are interested in permutations of the numbers from 1 to \( n \), where \( n \) is at least 4. The specific task is to determine the likelihood that in a randomly chosen permutation, the number 2 appears before the number 1. Understanding this problem can involve consideration of symmetry in permutations – essentially, when you reverse any permutation where 1 precedes 2, you get a permutation where 2 precedes 1, and vice versa. For further learning, examining sets of permutations and practicing with different values of \( n \) is encouraged. ---
Transcribed Image Text:**Educational Content: Probability in Permutations** --- **Title: Understanding Probability in Permutations** **Section 1: Problem Overview** **Question:** What is the probability of selecting a permutation in which 2 precedes 1? **Context:** Consider the set of all permutations of \( \{1, 2, \ldots, n\} \) where \( n \geq 4 \). This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. **Section 2: Answer Choices** **Multiple Choice Options:** - \( \frac{1}{4} \) - \( 1 \) - \( \frac{1}{2} \) - \( \frac{1}{3} \) **Section 3: Explanation of Concepts** Permutations of a set refer to all possible arrangements of its elements. Here, we are interested in permutations of the numbers from 1 to \( n \), where \( n \) is at least 4. The specific task is to determine the likelihood that in a randomly chosen permutation, the number 2 appears before the number 1. Understanding this problem can involve consideration of symmetry in permutations – essentially, when you reverse any permutation where 1 precedes 2, you get a permutation where 2 precedes 1, and vice versa. For further learning, examining sets of permutations and practicing with different values of \( n \) is encouraged. ---
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