A-LevelMathematicsProbability and statistics9709/63 · Oct/Nov 2019 · Q36 Marks
A sports team of 7 people is to be chosen from 6 attackers, 5 defenders and 4 midfielders. The team must include at least 3 attackers, at least 2 defenders and at least 1 midfielder.
- (i)In how many different ways can the team of 7 people be chosen?[4]
- (ii)The team of 7 that is chosen travels to a match in two cars. A group of 4 travel in one car and a group of 3 travel in the other car. In how many different ways can the team of 7 be divided into a group of 4 and a group of 3?[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [M1] Cxx C x ⁴Cz, x + y + z = 7
- [A1] 2 correct products, allow unsimplified
- [M1] Summing their totals for 3 correct scenarios only
- [A1] Correct answer
- [SC1] 6C3 × 5C2 × 4C1 × 1C1 = 7200
- [B1] ⁷C₄ or ⁷C₃ seen anywhere
- [B1] 35
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