121 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 27 .

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 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?