Question on probability

Question

Quen: In a pharmaceutical study, two drugs (A and B) and a placebo are to be compared for effects. Fifty people are to be used in the study, of whom 20 are to receive drug A, 20 receive drug B, and the remainder receive the placebo. Assuming the people are numbered 1 to 50, how many different ways could the assignment of the drugs and placebo be made?

Answer 1

Well you can choose the drug A group in C (50,20) ways as you choose 20 out of 50

Then in the remaining 30 people, you can choose the drug B group in C(30, 20) ways.

The placebo group is then determined.

So number of different ways = C (50,20) x C (30,20)