A certain make of car comes equipped with an engine in one of four sizes (in liters): 2.8, 3.0, 3.3, or 3.8. Ten percent of customers order the 2.8 liter engine, 40% order the 3.0, 30% order the 3.3, and 20% order the 3.8. A random sample of 20 orders is selected for audit.
a. What is the probability that the numbers of orders for the 2.8, 3.0, 3.3, and 3.8 liter engines are 3, 7, 6, and 4, respectively?
b. What is the probability that more than 10 orders are for 3.0 liter engines?