Question 4.11: Fruit Juice Shelf Display Study A company produces fruit jui......
Fruit Juice Shelf Display Study
A company produces fruit juice in 10 different flavours. A local supermarket sells the product, but has only sufficient shelf space to display three of the company’s 10 fruit juice flavours at a time.
(a) How many possible groupings (combinations) of three flavours can the fruit juice company display on the local supermarket shelf ?
(b) What is the probability that a particular combination of three fruit juice flavours will be selected by the juice company for display?
(a) The order in which the three fruit juices flavours are chosen for display is not important, hence apply the combination Formula 4.12.
Given n = 10 fruit flavours, and r = 3 flavours for display.
Then _{10}C_{3} =\frac{10!}{3!(10-3)!} =\frac{10!}{3!\ 7!} =\frac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{(3\times 2\times 1)(7\times 6\times 5\times 4\times 3\times 2\times 1)} = 120 combinations
There are 120 different displays of three fruit juice flavours at a time that can be selected from a possible 10 flavours, without regard to order.
(b) The probability of selecting a particular combination of three fruit juice flavours out of a possible 10 flavours is:
P(any one combination of 3 flavours out of 10 flavours) = \frac{1}{120} = 0.0083
There is only a 0.83% chance that a particular combination of three fruit juice flavours will be selected.