Let suppose the following scenario

A manager decides that he wants to hire three people to his workplace. The applicant

pool consists of 10 men and 20 women. He doesn't want to show any favoritism towards a gender group,

which is why he selects the three people at random (they are equally likely to be selected).

Part A

Let the random variable

Y= the number of men in the hired category. What is the probability

distribution of Y ?

Part B

Check that the distribution ofYis indeed a valid probability distribution. Show your work