Question: The research and development department of a manufacturing concern is made up of sixteen professional engineers, six females and ten males. The owner wishes to select a group of five engineers from this department for the execution of a certain task.

(a) If the engineers were randomly selected what is the probability that three or more will be female.

(b) Find the probability that at most four members of the task force will be male.

(c) Let X denote the number of males in a group of five engineers randomly selected from the department under consideration. Find the probability distribution of X. Then compute E(X) and Var(X).