Choosing portable grill displays. Refer to the Journal of Consumer Research (March 2003) study of how people attempt to influence the choices of others, Exercise 3.27 (p. 122). Recall that students selected three portable grill displays to be compared from an offering of five different grill displays.
a. Use a counting rule to count the number of ways the three displays can be selected from the five available displays to form a three-grill-display combination.
b. The researchers informed students to select the three displays in order to convince people to choose Grill #2. Consequently, Grill #2 was a required selection. Use a counting rule to count the number of different ways the three grill displays can be selected from the five displays if Grill #2 must be selected. (Your answer should agree with the answer in 3.27a.)
c. Now suppose the three selected grills will be set up in a specific order for viewing by a customer. (The customer views one grill first, then the second, and finally the third grill.) Again, Grill #2 must be one of the three selected. How many different ways can the three grill displays be selected if customers view the grills in order?
Exercise 3.2
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Choosing portable grill displays. University of Maryland marketing professor R. W. Hamilton studied how people attempt to influence the choices of others by offering undesirable alternatives ( Journal of Consumer Research , Mar. 2003). Such a phenomenon typically occurs when family members propose a vacation spot, friends recommend a restaurant for dinner, and realtors show the buyer potential home sites. In one phase of the study, the researcher had each of 124 college students select showroom displays for portable grills. Five different displays (representing five different-sized grills) were available, but only three would be selected. The students were instructed to select the displays to maximize purchases of Grill #2 (a smaller grill).
a. In how many possible ways can the three-grill displays be selected from the 5 displays? List the possibilities.
b. The next table shows the grill display combinations and number of each selected by the 124 students. Use this information to assign reasonable probabilities to the different display combinations.
c. Find the probability that a student who participated in the study selected a display combination involving Grill #1.