how many different ways are there to arrange five distinct objects in a row?
As illustrated before for 5 objects, the number of ways to pick from 5 objects is 5! . Note that your choice of 5 objects can take any order whatsoever, because your choice each time can be any of the remaining objects. So we say that there are 5 factorial = 5! = 5x4x3x2x1 = 120 ways to arrange five objects.