Counting Principle - Dependent Events There are 7 red and 5 yellow fish in an aquarium. Three fish are randomly caught in a net. Find the probability that the fish were:
a)  All red
b)  Not all of the same color.
I have solved this question using the method for dependent events as follows:
a)  $\frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{210}{1320}$
b)  $1 - \left(\frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} + \frac{5}{12} \cdot \frac{4}{11} \cdot \frac{3}{10}\right) = \frac{1170}{1320}$
Is it possible to use combinations to solve this question? If yes, how?

a) $$\frac{\binom73\binom50}{\binom{12}3}$$
b) $$1-\frac{\binom73\binom50}{\binom{12}3}-\frac{\binom70\binom53}{\binom{12}3}$$
