If you have NN different objects that you would like to position into NN different places, you can put the first object to any one of the NN available places.
Then, with each of the NN positions of the first object, the second object can be placed into any one of the remaining N-1N−1 places. That makes the number of available position of the first two objects equal to N*(N-1)N⋅(N−1).
With each of the N*(N-1)N⋅(N−1) positions of the first two objects there are N-2N−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)N⋅(N−1)⋅(N−2).
Continuing this logic, we come to conclusion that all NN objects can be positioned in
N * (N-1) * (N-2) *...*2*1 = N! ways.
