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 homes. 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 displays would be selected. The students were instructed to select the displays to maximize purchases of Grill #2 (a smaller-sized grill).
a. In how many possible ways can the three grill displays be selected from the five displays? List the possibilities.
b. The table shows the grill display combinations and the 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.

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Grill Display Combination Number of Students 35 42 1-2-3 1-2-4 1-2-5 2-3-4 2-3-5 2-4-5 34