O-LevelAdditional MathematicsPermutations and combinations4037/21 · May/June 2025 · Q35 Marks
A sports club has the following members. 5 runners, 4 swimmers, 3 gymnasts
- (a)These members stand in a straight line. Find the number of ways that this can be done when all the runners stand together, all the swimmers stand together and all the gymnasts stand together.[2]
- (b)Four of these members are selected for an event. Find the number of ways that this can be done when at least one runner, at least one swimmer and at least one gymnast must be selected.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [M1] for k × 5! × 4! × 3! where k = 1, 2, 3, 6
- [A1] 103 680
- [M2] for ⁵C₁ x ⁴C₁ x ³C₂ + ⁵C₁ x ⁴C₂ x ³C₁ + ⁵C₂ x ⁴C₁ x ³C₁ oe
- OR
- [M1] for at least one correct product
- If 0 scored then SC1 for a final answer of 540 or 264
- [A1] 270
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