1. A company places 3 digit serial numbers on each part that is made. Any number between 0 and 9 may be used in the digits. How many different serial numbers are possible if a. Digits can be repeated? b. Digits cannot be repeated? 2. Roulette is played at a table similar to the one in Figure 3.22. A wheel with the numbers 1 through 36 (evenly distributed with the colors red and black) and two green numbers 0 and 00 rotates in a shallow bowl with a curved wall. A small ball is spun on the inside of the wall and drops into a pocket corresponding to one of the numbers. Players may make 11 different types of bets by placing chips on different areas of the table. These include bets on a single number, two adjacent numbers, a row of three numbers, a block of four numbers, two adjacent rows of six numbers, and the five number combinations of 0, 00, 1, 2, and 3; bets on the numbers 1–18 or 19–36; the first, second, or third group of 12 numbers; a column of 12 numbers; even or odd; and red or black. Payoffs differ by bet. For instance, a single‐number bet pays 35 to 1 if it wins; a three‐ number bet pays 11 to 1; a column bet pays 2 to 1; and a color bet pays even money. Define the following events: C1 = column 1 number, C2 = column 2 number, C3 = column 3 number, O = odd number, E = even number, G = green number, F12 = first 12 numbers, S12 = second 12 numbers, and T12 = third 12 numbers. a. Find the probability of each of these events. b. Find P ( G or O ), P ( O or F 12), P ( C 1 or C 3), P ( E and F 12), P ( E or F 12), P ( S 12 and T 12), and P ( O or C 2).