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CA Foundation · Quantitative Aptitude · Permutations and Combinations

A student must answer 6 questions out of 10 in a paper, and must choose at least 4 from the first 5 questions. In how many ways can the student choose the questions?

The correct count is 55, so none of the listed values is right.

  1. A150Correct
  2. B110
  3. C126
  4. D135

Explanation

Exactly 4 from the first five: 5C4 × 5C2 = 5 × 10 = 50. Exactly 5 from the first five: 5C5 × 5C1 = 5. Total = 55... recompute: 6 questions total, so 4 from first and 2 from last: 5×10 = 50; 5 from first and 1 from last: 1×5 = 5. Total = 55.

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