Question

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

a) In how many different ways ca 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) The number of ways in which we can arrive at the final ranking is 10*9*8=720

This is becausei have 10 companies and if i wish to choose the best that is 1st amongst all the 10 companies i have all 10 options available, now to choose 2nd best i have only 9 options available and similarly only 8 while choosing the 3rd company.

b)To choose 3 among the 10 companies the number of options available are :

Hence there are 120 ways to choose 3 to be designated as top 3 companies.

c) To find the probability that atleast 1 of the company brand is selected out of the 2.

This is equal to 1-P(None of the brand of company X is selected)

Hence the probability of atleast one of the brand of company X is in top 3 is 8/15.

d) as company Z has 1 brand and 3 positions are available.

So the probability that, that brand would be in top 3 is 3/10=0.3.