Question

How many different ways can 12 people line up to go to the same bathroom

Answer 1

There are 12! ways to line 12 people up.  That is 12 factorial (the name for the exclamation point
12! means 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Using a scientific calculator to compute 12!, we get 479,001,600 ways to line up 12 people.  I know it sounds amazing but here is a chart.

People            Ways

3                       6
4                      24  (Notice that if you multiply 6 x 4 you get 24)
5                     120  (Notice that if you muliply 24 x 5 you get 120  etc.)
6                     720
7                     5040
8                    40,320
9                    362,880
10                 3,628,880
11               39,916,800
12               479,001,600