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:

For questions involving sequences of choices (like answering multiple-choice questions, forming numbers from digits, etc.), the multiplication principle is your go-to tool. Just multiply the number of options available for each position or step.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem uses the fundamental principle of counting (also known as the multiplication principle). For a sequence of independent events, the total number of possible outcomes is the product of the number of outcomes for each event.
Step 2: Key Formula or Approach:
If there are \(n_1\) ways for the first event, \(n_2\) for the second, ..., and \(n_k\) for the \(k\)-th event, then the total number of ways for the sequence of events to occur is \(n_1 \times n_2 \times \dots \times n_k\).
Step 3: Detailed Explanation:
For Column A:
There are 6 questions.
Each question has 5 choices.
The choice for each question is an independent event.
Total ways = (Ways for Q1) \( \times \) (Ways for Q2) \( \times \) ... \( \times \) (Ways for Q6)
\[ \text{Total ways} = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 5^6 \] \[ 5^6 = 15625 \] For Column B:
There are 5 questions with a varying number of choices.
Question 1 has 3 choices.
Question 2 has 4 choices.
Question 3 has 4 choices.
Question 4 has 5 choices.
Question 5 has 5 choices.
Using the multiplication principle:
\[ \text{Total ways} = 3 \times 4 \times 4 \times 5 \times 5 \] \[ \text{Total ways} = 3 \times 16 \times 25 = 48 \times 25 = 1200 \] Step 4: Final Answer:
Comparing the two quantities:
Quantity A = 15625
Quantity B = 1200
Therefore, Quantity A is greater than Quantity B.