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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?

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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.

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  • $\begingroup$ Multinomial coefficient? Ok, thx $\endgroup$ – milos Apr 5 '14 at 14:35

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