A panel containing five on-off switches in a row is to be set. Assuming no restrictions on individual switches, use the fundamental counting principle to find the total number of possible panel settings.
The total number of possible panel settings is (Type a whole number.)
Answer
Final Answer: The total number of possible panel settings is \(\boxed{32}\).
Step 1 ：Each switch has two possible states: on or off. Since there are five switches and each one operates independently of the others, we can use the fundamental counting principle to find the total number of possible settings. The fundamental counting principle states that if there are m ways to do one thing and n ways to do another, then there are m*n ways to do both. In this case, there are 2 ways to set each switch and 5 switches, so there are \(2*2*2*2*2 = 2^5\) ways to set all the switches.
Step 2 ：Final Answer: The total number of possible panel settings is \(\boxed{32}\).
