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:

Pay close attention to keywords like "different" or "any". "Different" implies non-repetition and reduces the number of choices for subsequent events. "Any" implies repetition is allowed.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This problem involves the fundamental principle of counting for a sequence of two events: the journey from city A to B, and the return journey from B to A. The key difference between the two columns is the restriction placed on the return journey.
Step 2: Key Formula or Approach:
We will use the multiplication principle. The total number of ways is the product of the number of choices for the first part of the journey and the number of choices for the second part.
Step 3: Detailed Explanation:
For Column A:
A man goes from city A to B and returns by a different bus.
Number of choices to go from A to B = 5 (he can take any of the 5 buses).
Since he must return by a different bus, the bus he took to go is not an option for the return trip.
Number of choices to return from B to A = \(5 - 1 = 4\).
Total number of ways = (Choices for going) \( \times \) (Choices for returning)
\[ \text{Total ways} = 5 \times 4 = 20 \] For Column B:
A man goes from city A to B and returns by any of the five buses.
Number of choices to go from A to B = 5.
There is no restriction on the return bus; he can even take the same bus back.
Number of choices to return from B to A = 5.
Total number of ways = (Choices for going) \( \times \) (Choices for returning)
\[ \text{Total ways} = 5 \times 5 = 25 \] Step 4: Final Answer:
Comparing the two quantities:
Quantity A = 20
Quantity B = 25
Therefore, Quantity B is greater than Quantity A.