An urn contains seven red balls, seven white balls, and seven blue balls. A sample of five balls is drawn at random without replacement. Compute the probability that:
E = The sample contains at least one ball of each colour.
The answer is:
$$P(E) = \frac{C(3,1)×C(7,3)×C(7,1)×C(7,1)+C(3,2)×C(7,2)×C(7,2)×C(7,1)}{C(21,5)}$$
But I don't get how they calculated the numerator, what are the two separate events?