Question

You and five friends are posing for a photograph.In how many ways can you pose in a line for a photograph?

Answer 1

`6! = 6*5*4*3*2*1 = 720`

Explanation:

If you have `N` different objects that you would like to position into `N` different places, you can put the first object to any one of the `N` available places.

Then, with each of the `N` positions of the first object, the second object can be placed into any one of the remaining `N-1` places. That makes the number of available position of the first two objects equal to `N*(N-1)`.

With each of the `N*(N-1)` positions of the first two objects there are `N-2` available positions for the third object. That makes the number of possible positions of the first three objects equal to `N*(N-1)*(N-2)`.

Continuing this logic, we come to conclusion that all `N` objects can be positioned in
`N * (N-1) * (N-2) *...*2*1 = N!` ways.