Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

Within an orchestra, there are 11 violinists, 5 cellists and 4 double bass players. A group of 6 musicians is to be chosen from these 20.
(i)[4]

How many distinct ways are there to choose 6 musicians if the selection must include at least 4 violinists, at least 1 cellist and at most 1 double bass player?

(ii)[3]

The chosen group of 6 musicians contains 4 violinists, 1 cellist and 1 double bass player. They are lined up for a concert. How many different arrangements are possible if the violinists have to sit together?

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct use of combinations for the cases, for example $^ {11}C_4\times{}^5C_1\times{}^4C_1$

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