O-LevelAdditional MathematicsPermutations and combinations4037/21 · May/June 2017 · Q87 Marks
A football club has 30 players. In how many different ways can a captain and a vice-captain be selected at random from these players?
- (a)A football club has 30 players. In how many different ways can a captain and a vice-captain be selected at random from these players?[1]
- (b)(i)A team of 11 teachers is to be chosen from 2 mathematics teachers, 5 computing teachers and 9 science teachers. Find the number of different teams that can be chosen if the team must have exactly 1 mathematics teacher,[2]
- (b)(ii)A team of 11 teachers is to be chosen from 2 mathematics teachers, 5 computing teachers and 9 science teachers. Find the number of different teams that can be chosen if the team must have exactly 1 mathematics teacher and at least 4 computing teachers.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B1] [³⁰P₂ =] 870
- [M1] ²C₁ × ¹⁴C₁₀ oe (2 × 1001) Condone (14 choose 10)
- [A1] 2002 implies M1
- [M3] (²C₁ × ⁵C₄ × ⁹C₆) + (²C₁ × ⁵C₅ × ⁹C₅) oe (840 + 252) M3 for fully correct method soi M2 for all necessary products but not summed with no extra products seen soi M1 for one correct three term product soi
- [A1] 1092 implies M3
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