Mathematics 9709 · AS & A Level · Permutations and combinations
Permutations and combinations — practice question
Out of a class of $21$ students, $10$ are violinists, $6$ are guitarists and $5$ are pianists. A set of $7$ is to be selected from these $21$ students. The set will contain $4$ violinists, $2$ guitarists and $1$ pianist.
(a)[2]
How many different ways are there to select the group of $7$?
(b)[4]
At a different time, a group of $5$ is to be selected from the $21$ students. The group must include at least $2$ violinists, at least $1$ guitarist and at most $1$ pianist. In how many ways can the group of $5$ be selected?
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Appropriate application of combinations $\binom{10}{4}\binom{6}{2}\binom{5}{1}$” …