Final Answer:
If at least one switch on Pamela's computer printer must be off, she can select a total of 31 different settings.
Step-by-step explanation:
To find the number of different settings that Pamela can select if at least one switch must be off, we can use the formula for combinations (C). This formula calculates the number of ways to select a certain number of items from a larger set, with no regard for the order in which they are selected. The formula is:
C(n, k) = n! / (k! * (n - k)!)
In this case, there are five switches (n = 5), and at least one switch must be off (k = 4). We can calculate the number of different settings as follows:
C(5, 4) = 5! / (4! * 1!) = 5
This means that if Pamela turns off exactly one switch, she can select from four remaining switches, for a total of five different settings. However, we also need to consider the fact that Pamela could turn off any combination of switches, not just exactly one. To account for this, we can use the formula for total combinations (Ct):
Ct(n, k) = C(n, k) + C(n, k-1) + ... + C(n, 1) + C(n, 0)
In this case, we want to find the total number of combinations where at least one switch is off (k > 0). This can be calculated as follows:
Ct(5, >0) = C(5, 4) + C(5, 3) + C(5, 2) + C(5, 1) + C(5, 0) = 31
Therefore, Pamela can select a total of 31 different settings if at least one switch must be off. This means that she has a wide range of options to choose from when customizing her computer printer's settings.