Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
A team of 7 players is to be selected from 6 attackers, 5 defenders and 4 midfielders. The team has to contain at least 3 attackers, at least 2 defenders and at least 1 midfielder.
(i)[4]
How many different selections of 7 people are possible for the team?
(ii)[2]
The selected team of 7 goes to a match in two cars. Four travel in one car and 3 travel in the other car. In how many different ways can the team of 7 be split into a group of 4 and a group of 3?
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate use of combinations like ${}^6C_x {}^5C_y {}^4C_z$ with $x+y+z=7$ for the valid cases” …