Binary-answer test sequences: A test has 10 questions, each answered True (T) or False (F). Every candidate answers all questions. How many distinct T/F answer sequences are possible?

Introduction / Context:
Each question admits 2 choices (T or F), independently across questions. Counting sequences of independent binary choices leads to a simple power rule, 2^n for n questions.

Given Data / Assumptions:

• n = 10 questions.
• Choices per question = 2 (T or F), independent.
• Every candidate answers all questions.

Concept / Approach:

• Use the multiplication principle: 2 * 2 * … * 2 (10 times) = 2^10.

Step-by-Step Solution:

Verification / Alternative check:
Binary coding analogy: each sequence corresponds to a 10-bit string; total 10-bit strings = 2^10 = 1024.

Why Other Options Are Wrong:

• 512 = 2^9; too small.
• 20 and 40 are unrelated to 2^10.

Common Pitfalls:

• Treating “questions” as dependent when they are independent.

Final Answer:
1024