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

Jul 2, 2016

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 $N \cdot \left(N - 1\right)$.

With each of the $N \cdot \left(N - 1\right)$ 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 $N \cdot \left(N - 1\right) \cdot \left(N - 2\right)$.

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