The name for equations/problems like "How many four-digit numbers have four different digits (without a leading $0$)?" I'm not very quick at these kinds of problems so I want to improve on them. But I don't know what topics to search for. 
Should I be searching for significant figures + base arithmetic?

How many four-digit decimal numbers are made from four (4) different digits between $0$ and $9$?
Here, a four-digit decimal number has a non-zero leading digit.


As you were told in the comments, the topic is called permutation. But, as you don't the whole set of digit numbers some may refer to that as an variation on some texts. I have read that a variation is a permutation of r elements from n. By this definition we could get the closed formula,
$$V(n,r)=\frac{n!}{(n-r)!}.$$
This term is introduced because some people link the idea of permutation to the factorial.
To solve your example this "new" idea should be use with the multiplication principle as follows,
$$9\times V(9,3)$$
First you choose the first digit (9 possibilities) and then reduce the problem to choose a number with three digits (it could be a zero leading digit in this case).
