Liberal Arts Math

A. a computer interface for a Kawai digital studio piano has eight microswitches that can be set in either the “on” or “off” position. These switches must be set properly for the interface to work. In how many different ways can this group of switches be set?

B.If it takes two 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?

C. What are some other real-world examples that you can develop that are similar to the ones above?
Please include the name of the person or question to which you are replying in the subject line. For example, “Tom’s response to Susan’s comment.” ALSO REPLY TO ANOTHER STUDENT’S COMMENT BELOW ⬇️⬇️⬇️⬇️⬇️

                       
A) Since there are 8 switches that can be set in 2 positions each I would take 2 to the 8th power or 2x2x2x2x2x2x2x2=256.Therefore there are 256 different ways to set the switches.
B) If it takes 2 minutes to set the switches the longest possible time would be, 2×256=512 minutes.
C) Another real world example of this could be – if you were taking a test with 10 questions and each question had 3 possible answers, how many different ways can you answer the 10 questions? If it takes you 1 minute per question how many minutes would it take to answer all 10 questions in all the different permutaions?

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