Solve both questions hand written and show work

1. Three events A, B, and C are shown on the Venn diagram in the following figure Reproduce the figure and shade the region that corresponds to each of the following events a) BUC (5 points) b) AnBUC (10 points) C) (AnC)U(AnB) (10 points) 2. A real estate agent is showing homes to a prospective buyer. There are nine homes in the desired price range listed in the area. The buyer has time to visit only four of them. a. In how many ways could the four homes be chosen if the order of visiting is considered? (5 points) b. In how many ways could the four homes be chosen if the order is disregarded? (5 points) c. If four of the homes are new and five have previously been occupied and if the four homes to visit are randomly chosen, what is the probability that all four are new? (Order is considered.) (10 points)