Combinations — A/L Combined Mathematics

How do I practise Combinations?

1 question with a worked solution

Check before you answer: Permutation vs Combination Selection: Choosing combinations (ⁿC_r) when order does not matter (committees, hands of cards, subsets) and permutations (ⁿP_r) for ordered arrangements.

1. From a group of 7 candidates, in how many distinct ways can a committee of 3 members be selected?
   1. A) 35
   2. B) 42
   3. C) 21
   4. D) 210
   Check my answer

   Correct answer: A) 35

   Since the order of members within the committee does not matter, this is a combination problem: ⁷C₃ = 7! / (3! 4!) = (7 × 6 × 5) / (3 × 2 × 1) = 210 / 6 = 35 ways.

   Show worked solution

   Step 1: Formula: ⁿC_r = n! / (r!(n-r)!). Step 2: ⁷C₃ = (7 × 6 × 5) / 6 = 35. Answer: 35.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Combinations fit in the syllabus?

Year 2 · Term 1