# How many ways there are to paint the strip of n cells with 3 colors

How many ways there are to paint the strip of N cells, using R red cells, B blue cells, G green cells if R+G+B=N?

After painting the $N$ cells they can be ordered. This originally in $N!$ ways.
Exactly $R!G!B!$ orders produce the same colourpattern. So there are $$\frac{N!}{R!G!B!}$$ different patterns.