O-LevelAdditional MathematicsPermutations and combinations4037/22 · Oct/Nov 2016 · Q117 Marks
Mr and Mrs Coldicott have 5 sons and 4 daughters. All 11 members of the family play tennis. Six members of the family enter a tennis competition where teams consist of 4 males and 2 females. Find the number of different teams of 4 males and 2 females that could be selected if
- (i)there are no further restrictions,[2]
- (ii)Mr and Mrs Coldicott must both be in the team,[2]
- (iii)either Mr or Mrs Coldicott is in the team but not both.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.
- [B1] (i) Free choice: no. of ways 6C4 × 5C2 =15×10 6C4 × another "C, term only
- [B1] =150 ×C2 and answer or vice versa
- [B1] (ii) Both Mr and Mrs Coldicott 5C3 × 4C₁ = 10×4 5C3 × another "C, term only
- [B1] = 40 ×C₁ and answer or vice versa
- [B1] (iii) Mr C and not Mrs C 5C3 × 4C2 (= 60) An incorrect final answer does not affect the awarding of the first two B1 marks.
- [B1] Not Mr C and Mrs C 5C4 × 4C₁ (= 20)
- [B1] Total = 80 www
- OR
- [M1] Total = (i) – (ii) – neither
- [A1] Neither = 5C4 × 4C2 = 30
- [A1] Total = 150 – 40 – 30 = 80
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