Question

New car owners were asked to evaluate their experiences in buying a new car during the past 12 months. In the survey, the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick. When ranking the dealers, how many outcomes are possible?

Answer 1

The total number of combinations of n things is always 2^n. In this case n=3 (Subaru, Honda, and Buick) 2^3 = 8

So there are 8 possible outcomes/combinations

Explanation:

Answer 2

When ranking the dealers, the total possible outcomes are 6.

Explanation:

It is given that the owners were most satisfied with their experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick.

We need to find the total possible outcomes when ranking the dealers.

It means we need to arrange these 3 dealers.

According to permutation, the total possible ways to arrange n items is

`^nP_n=(n!)/(((n-n)!)=n!`

Total possible ways to rank three dealers is

`^3P_3=3!=3* 2* 1=6`

The total possible outcomes are 6. The list of possible ranking in ascending order is

1. Subaru, Honda, and Buick

2. Subaru, Buick, and Honda

3. Honda, Subaru, and Buick

4. Honda, Buick, and Subaru

5. Buick, Honda, and Subaru

6. Buick, Subaru, and Honda

Therefore, the total possible outcomes are 6.