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

Question

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?

Answer 1

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

Answer 2

You need to specify if you pick the three balls at the same time, or if you put them back before you pick the next one.

Edit : Sorry, the information was present but had been removed by the first reviewer... :-/