Question

It is required to rank the top three different brands of certain food products. A total of ten brands are to be included in the study.

a) In how many different ways can we arrive at the final ranking (top three products)?

b) In how many different ways can we choose the three to be designated as top products?

c) If company X has two brands in the group of ten, what is the probability that at least one of the company brands is selected in the top three through random selection?

d) What is the probability that a random company Z’s brand is ranked in the top three

Answer 1

a) Total number of ways to arrive at the final ranking = 10P3 = 10! / (10 - 3)! = 720

Here we use permutation, because order of selection is important

b) Total number of ways to choose top three products = 10C3 = 10! / (3! * (10 - 3)!) = 120

Here we use combination, because order of selection is not important

c) P(at least one of the company brands is selected in the top three) = 1 - P(none of the company brands is selected in the top three)

                                                            = 1 - (8C3 / 10C3)

                                                            = 1 - 56/120

                                                            = 64 / 120

                                                            = 8/15

d) P(random company Z’s brand is ranked in the top three) = 1C1 * 9C2 / 10C3 = 36 / 120 = 4/15