Question:
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Matching \(n\) items to \(n\) items is a direct application of permutations, resulting in \(n!\) possibilities. When a question asks for "wrong" outcomes, calculate the total outcomes and subtract the number of "correct" outcomes (which is usually 1).
Updated On: Oct 3, 2025
- The quantity on the left is greater
- The quantity on the right is greater
- Both are equal
- The relationship cannot be determined without further information
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
Both columns deal with a "match the following" scenario, which is a permutation problem. For \(n\) items in each column, there are \(n!\) total ways to match them. Column B adds a twist by asking for the number of *wrong* answers.
Step 2: Key Formula or Approach:
The number of ways to create a one-to-one matching between two sets of \(n\) items is \(n!\) (n factorial). Number of wrong answers = Total possible answers - Number of correct answers.
Step 3: Detailed Explanation:
For Column A:
There are 5 items in column A and 5 items in column B. The first item in column A can be matched with any of the 5 items in column B. The second item in column A can be matched with any of the remaining 4 items. This continues until the last item. The total number of possible ways to match (possible answers) is: \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \] So, Quantity A is 120.
For Column B:
There are 6 items in column A and 6 items in column B. First, we find the total number of possible answers, which is the total number of ways to match the columns. \[ \text{Total possible answers} = 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \] Assuming there is only one unique correct matching, the number of correct answers is 1. The number of possible wrong answers is the total number of answers minus the number of correct answers. \[ \text{Number of wrong answers} = 720 - 1 = 719 \] So, Quantity B is 719.
Step 4: Final Answer:
Comparing the two quantities:
Quantity A = 120
Quantity B = 719
Quantity B is greater than Quantity A.
Both columns deal with a "match the following" scenario, which is a permutation problem. For \(n\) items in each column, there are \(n!\) total ways to match them. Column B adds a twist by asking for the number of *wrong* answers.
Step 2: Key Formula or Approach:
The number of ways to create a one-to-one matching between two sets of \(n\) items is \(n!\) (n factorial). Number of wrong answers = Total possible answers - Number of correct answers.
Step 3: Detailed Explanation:
For Column A:
There are 5 items in column A and 5 items in column B. The first item in column A can be matched with any of the 5 items in column B. The second item in column A can be matched with any of the remaining 4 items. This continues until the last item. The total number of possible ways to match (possible answers) is: \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \] So, Quantity A is 120.
For Column B:
There are 6 items in column A and 6 items in column B. First, we find the total number of possible answers, which is the total number of ways to match the columns. \[ \text{Total possible answers} = 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \] Assuming there is only one unique correct matching, the number of correct answers is 1. The number of possible wrong answers is the total number of answers minus the number of correct answers. \[ \text{Number of wrong answers} = 720 - 1 = 719 \] So, Quantity B is 719.
Step 4: Final Answer:
Comparing the two quantities:
Quantity A = 120
Quantity B = 719
Quantity B is greater than Quantity A.
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