I had figured out factorials on my own, but only to a point. There is only one way to order one object, but a second object can be in front of or behind it. A third object can be in front of, in between the other two, or after. Adding more increases the number of "in betweens". When the topic was taught to me, there were n places to put the first object, n - 1 spots for the 2nd, down to 2 spots for the penultimate object and the last one goes into the last slot. That model could handle combinations which mine couldn't.