A health inspector must visit 4 of 9 restaurants on Monday I

A health inspector must visit 4 of 9 restaurants on Monday. In how many ways can she pick a first, second, third, and fourth restaurant to visit?

There are __ ways.

Solution

There are 9 ways for the first slot, 8 for the second, 7 for the third and 6 for the fourth. So there are 9*8*7*6 = 3024 ways to visit them.

Here we have assumed that the order of the restaurants matter.

If the order doesn\'t matter, then there are really 3024/(4!) = 3024/24 = 126 ways.

In my opinion, the order doesn\'t matter as each restaurant is given the same treatment and inspection (regardless of which comes first). So I\'d say that the answer is 126.