# Extended permutations, what if you keep adding categories? [duplicate]

'm a little bit unsure how to approach this problem of permutations when you add categories:

Each object can contain 3 attributes out of the 10 possible available.

Because order doesn't matter, there would be 10 x 9 x 8 = 720 possible choices. If duplications of attributes don't matter (eg. you can have 3 of the same attribute), then there will be 10 x 10 x 10 possible choices. This part is easy.

But what I don't understand, is what happens if this object can randomly come from any of 30 countries? And what if this object can be of any 5 sizes? (These are not attributes mentioned before)

How many possibilities are there?

That's not right, actually. That would be the number if order did matter. If order doesn't matter, the number is $\binom{10}{3}=120$.
So if there are $10$ attributes, $3$ are randomly chosen, no repeats, and there can be 30 countries of origin and 5 sizes, then there are
$\displaystyle\binom{10}{3}*30*5=18000$ possibilities.