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Nov 2018 p61 q3
2773
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.
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?
Solution
Treat the 4 violinists as a single unit or 'block'. This means we have 3 units to arrange: the 'block' of violinists, 1 cellist, and 1 double bass player.
The number of ways to arrange these 3 units is given by:
\(3! = 6\)
Within the 'block' of violinists, the 4 violinists can be arranged among themselves in: