9. An engineer is scheduled to visit four manufacturing plants in CSU Piat, Cauayan, Ilagan, and Universal Robina Piat. a. How many different sequences or orders of visiting these four plants are possible? (1.5 points) b. In how many different orders can the 4 plants be visited if plants located in Piat can be considered identical? (1.5 points)

10. The number of students who fail per semester is often modeled as a Poisson random variable. Assume that on the average there are 6 students who fail per sem.

a. What is the probability that there are exactly 5 students who fail in 1 sem? (1 points)

b. What is the probability that there are exactly 3 students in one academic year? (1 points)

c. What is the probability that there are at least 3 students who fail in one sem? (2 points)

d. If exponential distribution can model this system, what is the probability that there will be no failing students right after midterm? Let X denote the time in semesters from the start of the interval until the first failure and that a semester is divided by midterm period. (2 points)

e. Calculate the probability that there will be a failing student within the first semester. (2 points) F. Calculate the probability that a failing student will be first spotted after midterm up to end of the first semester? (2 points