Question

• A. The quantity on the left is greater
• B. The quantity on the right is greater
• C. Both are equal
• D. The relationship cannot be determined without further information

Hint:

Recognize that problems involving assigning distinct jobs/posts/duties to an equal number of distinct people/candidates/students are permutation problems. The number of ways is simply \(n!\), where \(n\) is the number of jobs and people.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Both questions are about arranging a set of items (duties or posts) among an equal number of recipients (students or candidates). This is a classic permutation problem, as the order of assignment matters. For example, Student 1 getting Duty A is different from Student 1 getting Duty B.
Step 2: Key Formula or Approach:
The number of ways to arrange \(n\) distinct items among \(n\) distinct positions is given by the permutation formula \(P(n, n)\), which is equal to \(n!\) (n factorial).
\[ n! = n \times (n-1) \times (n-2) \times \dots \times 1 \] Step 3: Detailed Explanation:
For Column A:
We have 3 distinct duties (A, B, C) to be assigned to 3 distinct students.
The first duty can be given to any of the 3 students.
The second duty can then be given to any of the remaining 2 students.
The third duty must be given to the last remaining student.
Total number of ways = \( 3 \times 2 \times 1 = 3! = 6 \).
Alternatively, this is a permutation of 3 items taken 3 at a time, \(P(3, 3) = 3! = 6\).
For Column B:
We have 3 distinct posts to be filled by 3 distinct candidates.
This is functionally identical to the problem in Column A.
The first post can be filled by any of the 3 candidates.
The second post can be filled by any of the remaining 2 candidates.
The third post must be filled by the last remaining candidate.
Total number of ways = \( 3 \times 2 \times 1 = 3! = 6 \).
This is also a permutation of 3 items taken 3 at a time, \(P(3, 3) = 3! = 6\).
Step 4: Final Answer:
Comparing the two quantities:
Quantity A = 6
Quantity B = 6
The two quantities are equal.