How many possible orders?

[dstebbins]

If you have x number of unique items, and have to put them in an order, would there be x! possible orders? For example, if there are five unique items, are there 120 possible orders in which to place them, and, if there are ten unique items, there are 3,628,800 different orders, and so on and so forth.

 

Is that correct?

[ydoaPs]

Let's say there are 5 unique objects.

 

The first slot in the order can be any of the five. Now, we've eliminated a possible object for the second slot(the second object cannot be the first object). This means that there are only four possible object for the second slot after we have chosen a first. Choosing the second slot similarly limits the number of objects for the third slot and so on until you arrive at only one possible object for the last slot.

 

So, if X is the number of all possible orders of the five unique objects, then X=5x4x3x2x1=120.