Question

The local theater has one ticket window. In how many ways can six people line up to buy a ticket?

Answer 1

We must count the number of permutations of 6 people. There are 6 choices for the first person in line, 5 choices for the second person in line, etc. So the answer is 6 · 5 · 4 · 3 · 2 · 1 = 720.

Answer 2

720 ways

Explanation:

The first person in line could be any one of the 6 people

6

Then there are 5 people left

The second person in line could be any one of the 5 people

5

Then there are 4 people left

The third person in line could be any one of the 4 people

4

Then there are 3 people left

The fourth person in line could be any one of the 3 people

3

Then there are 2 people left

The fifth person in line could be any one of the2 people

2

Then there are 1 people left

The last person in line could be any one of the 1 people

1

6*5*4*3*2*1 =720 ways