1- Three research departments have 6 , 7 , and 8 members, respectively. If each department is to select a delegate and an alternate to represent the department at a conference, in how many ways can this be done?
2- From a group of 18 customers, 5 are to be chosen to receive a special gift. Assuming that the order in which the customers are chosen is irrelevant, how many groups of 5 customers can be chosen?
3- A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was 41 years old, with a standard deviation of 9 years. Suppose that these measures are valid for the population of all home buyers. Complete the following statements about the distribution of all ages of home buyers.
(a) According to Chebyshev's theorem, at least ____?% of the home buyers' ages lie between 18.5 years and 63.5 years.
(b) According to Chebyshev's theorem, at least ____?% of the home buyers' ages lie between 23 years and 59 years.
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ____?% of the home buyers' ages lie between 23 years and 59 years.
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the home buyers' ages lie between ____?% years and ____?%years