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 multiple-choice question problems, the formula is simply \((\text{choices per question})^{(\text{number of questions})}\). Be comfortable with calculating powers of small integers to solve these quickly.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem deals with the total number of ways to answer a series of multiple-choice questions. Since the choice for each question is independent of the others, we can use the fundamental principle of counting (multiplication principle).
Step 2: Key Formula or Approach:
If there are \(k\) independent events, and the \(i\)-th event can occur in \(n_i\) ways, then the total number of ways for the sequence of events is \(n_1 \times n_2 \times \dots \times n_k\). For \(k\) questions each with \(n\) choices, the total ways are \(n^k\).
Step 3: Detailed Explanation:
For Column A:
- There are 8 questions. - Each question is of the true-false type, meaning each has 2 choices (True or False). - Total number of ways = (Choices for Q1) \( \times \) (Choices for Q2) \( \times \dots \times \) (Choices for Q8) \[ \text{Total ways} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^8 \] \[ 2^8 = 256 \] So, Quantity A is 256.
For Column B:
- There are 5 questions. - Each question has 3 choices. - Total number of ways = (Choices for Q1) \( \times \dots \times \) (Choices for Q5) \[ \text{Total ways} = 3 \times 3 \times 3 \times 3 \times 3 = 3^5 \] \[ 3^5 = 243 \] So, Quantity B is 243.
Step 4: Final Answer:
Comparing the two quantities:
Quantity A = 256
Quantity B = 243
Quantity A is greater than Quantity B.