This is Statistics and Data Analysis :PROBABILITYAnswer the question.

9. What is the difference between the permutations rule and the combinations rule? HOW 10. A salesperson living in city A wishes to visit five cities B, C, D, E, and F. 6. Let S be the event that a randomly selected college student has taken a Geology subject, and let C be the event that the same student has taken a Physics subject. Suppose P(S) = 0.4, P(C) = 0.3, and P(S n C) = 0.2. a. Find the probability that a student has taken Geology, Physics, or both. b. Find the probability that a student has taken neither Geology nor Physics. c. Find the probability that a student has taken Geology but not Physics. 7. Suppose that a family is leaving on a summer vacation in their camper and that M is the event that they will experience mechanical problems, T is the event that they will receive a ticket for committing a traffic violation, and V is the event that they will arrive at a campsite with no vacancies. Referring to the Venn diagram, state in words the events represented by the following regions: a. region 5; (example: The family will experience mechanical problems but will receive no ticket for a traffic violation and will not arrive at a campsite that has no vacancies) b. region 3; c. regions 1 and 2 together; d. regions 4 and 7 together; e. regions 3, 6, 7, and 8 together. 8. Use the multiplicative rule to determine the number of sample points in the sample space corresponding to the experiment of tossing the following. a. a 4-sided die 4 times b. a 4-sided die 5 times c. a 4-sided die 6 times d. a 4-sided die n times a. If the cities are all connected by airlines, how many different travel plans could be constructed to visit each city exactly once and then return home? b. Suppose all cities are connected, except that D and E are not directly connected. How many different flight plans would be available to the salesperson