A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2018 · Q37 Marks
In an orchestra, there are 11 violinists, 5 cellists and 4 double bass players. A small group of 6 musicians is to be selected from these 20.
- (i)How many different selections of 6 musicians can be made if there must be at least 4 violinists, at least 1 cellist and no more than 1 double bass player?[4]
- (ii)The small group that is selected contains 4 violinists, 1 cellist and 1 double bass player. They sit in a line to perform a concert. How many different arrangements are there of these 6 musicians if the violinists must sit together?[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [M1] 11Cx5C × 4Cc, a+b+c=6,
- [B1] 2 correct unsimplified options
- [M1] Add 2 or 3 correct scenarios only
- [A1] Correct answer
- [M1] k multiplied by 3! or 4!, k an integer ≥ 1
- [A1] Correct unsimplified expression
- [A1] Correct answer
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