Multiple-choice test outcomes (not all correct): A paper has 4 MCQs, each with 5 options and exactly one correct choice. How many answer patterns result in not getting all four answers correct?

Introduction / Context:We count all possible answer patterns and subtract the single perfect pattern where all answers are correct. This is a straightforward application of the complement principle.

Given Data / Assumptions:

• 4 independent questions.
• Each question has 5 possible chosen options.
• Exactly one pattern corresponds to “all correct.”

Concept / Approach:

• Total patterns = 5^4.
• Subtract the one all-correct pattern.

Step-by-Step Solution:

Verification / Alternative check:Alternatively, sum by number wrong (≥ 1) is longer; complement is minimal and exact.

Why Other Options Are Wrong:

• 120 is unrelated (e.g., 5P3 * something).
• 1024 is 2^10 and not applicable.
• 19 is far too small.

Common Pitfalls:

• Forgetting that exactly one pattern achieves full correctness.

Final Answer:624