Mathematics 9709 · AS & A Level · Permutations and combinations

Permutations and combinations — practice question

Among 20 musicians, 9 are guitarists, 6 are pianists and 5 are drummers. From these 20, 6 musicians are chosen to perform at a concert.
(a)[4]

Determine the number of different selections of the 6 musicians if the selection must include at least 3 guitarists, at most 2 pianists and exactly 1 drummer.

(b)[3]

Three bands are to be selected from the original group of 20 musicians. Each band contains 3 guitarists, 1 pianist and 1 drummer. No musician may belong to more than one band. The first band selected will perform in France, the second band selected will perform in Italy and the third band selected will perform in Spain. Find the number of different ways in which these three bands can be selected.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Two valid scenario totals, for instance $^9C_3\,^6C_2\,^5C_1$ or an equivalent expression” …

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