Choosing portable grill displays. A study of how people attempt to influence the choices of others by offering undesirable alternatives was published in the Journal of Consumer Research (Mar. 2003). 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.
Grill Display Combination Number of Students 1–2–3 35 1–2–4 8 1–2–5 42 2–3–4 4 2–3–5 1 2–4–5 34 Based on Hamilton, R. W. “Why do people suggest what they do not want? Using context effects to influence others’ choices.” Journal of Consumer Research, Vol. 29, Mar. 2003, Table 1.