# What is the probability of selecting all three colors when $4$ balls are randomly selected from a box containing …?

What is the probability of selecting all three colors when $$4$$ balls are randomly selected from a box containing $$7$$ black, $$4$$ green and $$2$$ yellow balls?

• Hello @xxssxxdd, welcome to MSE. Questions in the style "here is the question, solve it" are not always well-received on MSE. Can you please add in the question what your attempts are? – Ernie060 Nov 10 '18 at 10:49

you can use combination formula to find out:$$p(3C)=p(2B+1G+1Y)+p(1B+2G+1Y)+(1B+1G+2Y)$$ $$=\frac{\binom{7}{2}\times \binom{4}{1}\times \binom{2}{1}}{\binom{13}{4}}+\frac{\binom{7}{1}\times \binom{4}{2}\times \binom{2}{1}}{\binom{13}{4}}+\frac{\binom{7}{1}\times \binom{4}{1}\times \binom{2}{2}}{\binom{13}{4}}$$ $$=\frac{56}{143}$$ Where $$3C=$$three colors, $$B$$=number of black ball,$$G=$$number of green ball,$$Y$$=number of yellow ball