What is the probability that a plant will be located in city C?

In statistics the words combination and permutation represent two different situations. Using the appropriate formulas clearly ilustrate and describe the difference in the meaning of these two words. Counting rules assist us in determining likelihood of different events occurring. Show through illustration the concept of counting rules with the following problem. You are tasked with locating three plants in the United States, one plant will be located in each of the three regions (East Coast, Midwest, West Coast). You have three possible East Coast cities (A,B,C) four Midwest cities (D,E,F,G) and two West Coast cities (H,I). What is the probability that a plant will be located in city C? What is the probability that plants will be located in cities A and H? Many probability density functions are modeled as declining exponentials such as ea with the assumption made that X greater than or equal to 0. Illustrate why you feel a distribution such as this is reasonable for many simulations. Can you provide examples of when this distribution might not be appropriate?

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