How many distinct three-digit numbers can be written with the digits $1$, $2$, $3$ and $4$ if no digit may be used more than once in a three-digit number?
Hint: Use constructive counting.
This is very similar to some of the other problems you have asked; try to make a connection so you know how to solve similar problems.
This is = the number of ordered sets formed by taking 3 objects from 4 =
P(4,3) = 24 sets