There is a Very Interesting Problem that illustrates how clever some of these "permutation with repeats" problems can get.

The Problem

Imagine there is a small car located at the origin of the $xy$-coordinate plane. The car can move in one-unit increments. How many distinct shortest routes can be taken by this car to the point $(5,4)$?

One possible route the car take

Check This Out

Notice that we can map out the car's route using letters: U for an "up" move and R for a "right" one.

And every single time, no matter the route, we have to move UP four times and move to the RIGHT five times. So we have this word: UUUURRRRR.

Now we know how to solve it! In how many ways can you distinctly arrange the letters UUUURRRRR?

$$\frac{9!}{4!5!} = 126$$