Question

A car manufacturing company asked 1000 people to view their latest two-door coupe available in four colors (White, Black, Cherry, and Blue).The viewers were asked to list their color preferences in order form favorite. How many ways could the colors be ordered? Of the 1000 viewers, how many would you expect to choose the following preference order: White, Black, Cherry, and Blue?

Answer 1

The first choice can be aby one of the 4 colors.

For each of these . . .

The 2nd choice can be any one of the 3 remaining colors.

For each of these . . .

The 3rd choice can be either one of the 2 remaining colors.

So there are (4 · 3 · 2) = 24 different ways to order the colors.

If everybody you ask thinks the same way, you'd expect all of the possible combinations to be chosen equal numbers of times . . . that is, every choice would be chosen once in every group of 24 people.

In 1,000 people, there are (1000/24) = (41 and 2/3) groups of 24 people.

So you'd expect any one possible preference order to be chosen by 41 or 42 viewers, if all of the viewers think the same way, and their preferences are perfectly random.