10 red 20 blue and 20 black if 5 are selected randomly and w

10 red, 20 blue, and 20 black
if 5 are selected randomly and without replacement. what is the probability that you pick 2 from red pens and 3 from blue pens

need an explanation with the answer

Solution

There are 50 pens in all. Thus, there are 50C5 ways to choose any 5 pens.

There are 10C2 ways to choose any 2 red, and 20C3 ways to choose three blue. Thuse, there are [(10C2)(20C3)] ways to do it.

Thus,

P = [(10C2)(20C3)]/(50C5) = 0.024212275 [ANSWER]