I think it is much worse than that. It has been awhile so please excuse me
if I don't remember the notation so I'll do this long hand. I can look up
the formula if you want but assuming you can use 2 of any item the one you
are looking for is sampling with single replacement. The problem isn't a
simple factorial problem because in many cases we are allowing items to
repeat. So it isn't 13x12...x6x5 one less for each slot of the box. In many
of the formulas I see people use two or more ingredients (i.e. 2xmetal rods)
Assuming that no item is used more than twice but that all items may be used
up to twice you would end up with a max of
13x13x12x12x11x11x10x10=294,465,600. Even if you assume only one component
can be used twice with up to 8 components with 13 possible choices you get
13x13x12x11x10x9x8x7=10,221,120

>I think the way you came up with that formula is good. (It must be, because
>it was what I came up with at first, lol)
>Problem is it is wrong.
>
>Suppose we have 13 types of items in 100 slots.
>
>That gives us 13^100/100! which is less than 1. (Can't be right.)
>
>The other problem I had with it is that it does not produce an integer
>number. What is 0.3 combinations?