Questions: Question 14 of 24 The total number of possible panel settings is (Type a whole number) A panel containing these 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 settings. Submit test Resume later This section's points possible The best 24 points possible The question's point(s) value

Solution Steps

To find the total number of possible panel settings with on/off switches, we can use the fundamental counting principle. Each switch has 2 possible states: on or off. If there are \( n \) switches, the total number of possible settings is \( 2^n \).

Let \( n \) represent the number of switches in the panel. In this case, we have \( n = 10 \).

According to the fundamental counting principle, each switch can be in one of two states: on or off. Therefore, the total number of possible settings for \( n \) switches is given by the expression:

\[ \text{Total Settings} = 2^n \]

Substituting \( n = 10 \) into the expression, we calculate:

\[ \text{Total Settings} = 2^{10} = 1024 \]

Final Answer