Mathematics 9709 · AS & A Level · Permutations and combinations
Permutations and combinations — practice question
The group of $12$ people is made up of $3$ boys, $4$ girls and $5$ adults.
(a)[2]
How many different ways are there to choose a team of $5$ people from the group if it contains exactly one adult?
(b)[4]
How many different ways can a team of $5$ people be selected from the group if it has at least $2$ boys and at least $1$ girl?
(c)[4]
How many distinct arrangements are possible if the $3$ boys stay together and an adult stands at each end of the line?
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct application of combinations, for example ${}^5C_1\times{}^7C_4$” …