A construction engineer has to inspect 5 construction sites in a 2-day inspection schedule. He may or may not be able to visit these sites in two days. He will not visit any site more than once.

(a) Using two coordinates so that \((3,1)\), for example, represents the event that he will visit 3 sites on Day 1 and 1 site on Day 2, draw a diagram similar to that of Figure 3.1 showing the points of the corresponding sample space.

(b) List the points of the sample space that constitutes the events \(X, Y\), and \(Z\) that he will visit only 2 sites on Day 2, he will visit all 5 sites, and he will visit more sites on Day 2 than on Day 1.

(c) Which of the three pairs of events, \(X\) and \(Y, Y\) and \(Z\), and \(X\) and \(Z\), are mutually exclusive?