# Combinatorics problem

So I found a formula for the number of ways of coloring a shape with 20 triangular faces, 30 edges, and 12 vertices: (1/60)*(k^20+15*k^10+20*k^8+24*k^4).

Now I need to find the # of ways of coloring the faces with exactly 5 colors each with each color used exactly 4 times. I know how to find the # of ways of coloring the faces with exactly 5 colors (just plug k=5 in the formula) But the part about "each color used exactly 4 times" is throwing me off. How do I do this?

$$\left( \begin{array}c 20 \\ 4 ~~ 4 ~~ 4 ~~ 4 ~~ 4 \end{array}\right) = \frac{20!}{4!\cdot4!\cdot4!\cdot4!\cdot4!}$$