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Let's break down the problem.

### Part (a):
You have 7 microswitches, and each can be set to one of two positions: "on" or "off." This is a classic case of binary choices.

For each switch, you have 2 possible settings: on or off. Since there are 7 switches, the total number of different ways they can be set is given by:

\[
2^7 = 128
\]

So, the answer to part (a) is that the group of switches can be set in **128 different ways.**

### Part (b):
It takes 3 minutes to test each possible combination of switch settings. Since there are 128 possible combinations, the total time to check all of them would be:

\[
128 \times 3 \text{ minutes} = 384 \text{ minutes}
\]

Now, convert 384 minutes into hours:

\[
384 \text{ minutes} = \frac{384}{60} = 6.4 \text{ hours}
\]

So, the longest possible time it would take is over **6 hours**. The correct answer is **C**.

Would you like further clarification on any part of the solution? 

Here are some related questions:
1. What happens if the number of microswitches is increased to 8?
2. How would the time change if it took 5 minutes per test?
3. How can we approach problems with more complex combinations, like switches with more than two positions?
4. What other real-life examples involve binary choices like this?
5. How would you calculate the time needed for a larger set of switches, say 10 switches?

**Tip**: For any problem involving binary choices, the total number of combinations is always \(2^n\), where \(n\) is the number of items (or switches, in this case).

A computer interface for a digital studio piano has seven microswitches that can be set in either the 'on' or 'off' position. These switches must be set properly for the interface to work. Answer questions (a) and (b).
a. In how many different ways can this group of switches be set?
b. If it takes 3 minutes to set the switches and test to see if the interface is working properly, what is the longest possible time that it would take to find the proper settings by trial and error? Choose the correct answer below.

This problem involves using combinatorics to calculate the different ways to set a group of switches with binary choices. Additionally, it includes calculating the time required to test all possible settings. A great exercise for students in Grades 7-9 covering basic counting principles.

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