In southern California, a growing number of persons pursuing a teaching credential are choosing paid internships over traditional student teaching programs. A group of eight candidates for three teaching positions consisted of five paid interns and three traditional student teachers. Let us assume that all eight candidates are equally qualified for the positions. Let x represent the number of paid interns who are hired for these three positions.
a. Does x have a binomial distribution or a hypergeometric distribution? Support your answer.
b. Find the probability that three paid interns are hired for these positions.
c. What is the probability that none of the three hired was a paid intern?
d. Find P(x ≤ 1).