Question

It is required to rank the top three different brands of a 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

From the given data,

Here,

a) Many different ways can we arrive at the final ranking.

= number of way to pick top three and arrange from 10 =(10P3)=10*9*8 =720

b) Many different ways can we choose the three to be designated as top products.

= number of ways =10C3 =10!/(3!*7!) =120

c) The probability that at least one of the company brands is selected in the top three through random selection.

= P(at least one ) =1-P(none is selected) =1-(8*7*6)/(10*9*8)=8/15

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

= P(ranked in top three) =3/10