Question

A marketing researcher is tasked with asking consumers about their opinions of 7 different varieties of instant mashed potato. Knowing that the order of presentation might influence perceptions of taste, she wants to present unique orders of the products to consumers. To save some time in testing, the researcher decides that she will select only three of the seven products for each person to sample. How many unique orders of three out the seven will be used in her testing?

Answer 1

210 unique orders of three out the seven will be used in her testing

Explanation:

Since the order is important, we can use the following interpretation to solve the problem:

We have these following three products.

P1 - P2 - P3

P1 can be any of the seven products. So, there are 7 options.

P2 can be any of the products, bar P1. So, there are 6 options.

P3 can be any of the products, bar P1 and P2. So, there are 5 options.

7*6*5 = 210.

210 unique orders of three out the seven will be used in her testing