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:

The number of ways to choose a mixed group (Column B) is just one part of the total ways to choose any group (Column A). The total ways also include choosing two boys or two girls, so it will always be larger.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This question compares two different ways of selecting monitors. Column A is a simple combination problem. Column B involves making selections from two distinct subgroups (boys and girls) and uses the multiplication principle.
Step 2: Key Formula or Approach:
The number of ways to choose \(r\) items from a set of \(n\) is \(C(n, r) = \frac{n!}{r!(n-r)!}\).
The multiplication principle states that if one event can occur in \(m\) ways and a second independent event can occur in \(n\) ways, the two can occur in \(m \times n\) ways.
Step 3: Detailed Explanation:
For Column A:
We need to choose 2 students from a class of 36. Since the roles are identical (both are "monitors"), the order does not matter. \[ \text{Number of ways} = C(36, 2) = \frac{36 \times 35}{2 \times 1} = 18 \times 35 = 630 \] So, Quantity A is 630.
For Column B:
We need to choose 1 girl from 18 girls AND 1 boy from 18 boys. - Ways to choose 1 girl from 18 = \(C(18, 1) = 18\). - Ways to choose 1 boy from 18 = \(C(18, 1) = 18\). Using the multiplication principle, the total number of ways is: \[ \text{Total ways} = 18 \times 18 = 324 \] So, Quantity B is 324.
Step 4: Final Answer:
Comparing the two quantities:
Quantity A = 630
Quantity B = 324
Quantity A is greater than Quantity B.