Choosing one question from each of three exercises: A test picks one question each from Exercise 7 (12 questions), Exercise 8 (18 questions), and Exercise 9 (9 questions). In how many ways can the three-question paper be formed?

Difficulty: Easy

Correct Answer: 1944

Explanation:

Introduction / Context:Selecting one item from each of several independent pools uses the multiplication principle. Here we choose one question from each of three exercises with given counts.

Given Data / Assumptions:

  • Exercise 7 has 12 questions.
  • Exercise 8 has 18 questions.
  • Exercise 9 has 9 questions.
  • Choices are independent.

Concept / Approach:

  • Total papers = 12 * 18 * 9.

Step-by-Step Solution:

12 * 18 = 216216 * 9 = 1944

Verification / Alternative check:No overlaps or constraints exist, so simple multiplication applies directly.

Why Other Options Are Wrong:

  • 2094, 1894, 2194 are arithmetic distractors, not equal to 12*18*9.

Common Pitfalls:

  • Adding the counts instead of multiplying across independent choices.

Final Answer:1944

More Questions from Permutation and Combination

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