Factorial of 0 - a convenience? If I am correct in stating that a factorial of a number ( of entities ) is the number of ways in which those entities can be arranged, then my question is as simple as asking - how do you conceive the idea of arranging nothing ? 
Its easy to conceive of a null element in the context of arrays, for example - so you say that there is only one way to present a null element. 
But, in layman terms - if there are three humans $h1, h2, h3$ that need to be arranged to sit on three chairs $c1, c2, c3$ - then how do you conceive of a) a null human, and b) to arrange those ( that ? ) null humans ( human ? ) on the three chairs ? 
Please note that referral to humans is just for easy explanation - not trying to be pseudo-philosophical. Three balls to be arranged on three corners of a triangle works just fine. So basically, how do you conceive of an object that doesn't exist, and then conceive of arranging that object ?
So, in essence ... is $0! = 1$, a convenience for mathematicians ? Not that its the only convenience, but just asking. Of course, there are many. 
If yes, then its a pity that I can't find it stated like so anywhere. 
If not, then can anybody suggest resources to read actual, good proofs ? 

I don't see any difficulty with the idea of "arranging a set of zero things"...
There is no need to 

conceive of an object that doesn't exist, and then conceive of arranging that object

mostly, because that does not make much sense at all.
If I give you 2 apples and I tell you to arrange them in a line above the table, there are 2 possible outcomes. If I give you zero apples, how many possible possible things can I find on the table after you are done? Exactly one: no apples on the table.
 
By the way, every definition in math is done out of convenience. 
