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Asked Jan 30, 2019

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Refer to the study below of how people attempt to influence the choices of others. 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 is selected. (The answer should agree with the answer of a)

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?

Step 1

**a. Find the number of ways in which the three displays can be selected from the five available displays to form a three grill display combination.**

** **The total number of displays is 5.

The number of displays that have to be selected to form a grill display is 3.

Combinations rule is used to select 3 displays among a total of 5 displays.

The number of ways in which the three displays can be selected from the five available displays to form a three grill display combination is obtained as 10 from the calculation given below:

Step 2

**b. Find the number of different ways in which the three grill displays can be selected from the five displays if grill #2 is selected.**

Among a total of 5 displays, in the required combination of 3 grill displays, grill#2 is fixed in all combinations.

Now, 2 displays have to be selected from the remaining 4 displays. The combinations rule is used to select 2 displays among 4 displays.

The number of different ways in which the three grill displays can be selected from the five displays if grill #2 is selected is obtained as 6 from the calculation given below:

Step 3

**c. Find the number of different ways in which the three grill displays be selected if customers view the grills in order with grill#2 as default.**

Here, it is given that the three selected grills will be set up in a specific order for viewing by a customer. The customer views the 3 grills one after one. Moreover, it is given that, grill #2 must be one of the three selected.

From this, it can be said that the grill#2 will be in any of the 3 positions (1, 2 or 3). Now the 2 displays have to be selected from the remaining 4 displays considering the...

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