Question

The frequency setting for a garage door opener is determined by the positions of ten switches, each of which can be set to a "+" or "-" position. In how many ways can the switches be set?

Answer 1

There are 1024 possible ways the switches can be set.

Step-by-step explanation:

The number of ways the switches can be set is determined by the number of possible positions for each switch. Since each switch can be set to either a '+' or '-' position, there are 2 possible positions for each switch. Since there are 10 switches in total, the number of possible ways the switches can be set is 2^10 = 1024.

Answer 2

Each switch has 2 possible positions ("+" or "-"), so the total number of ways to set all 10 switches is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2, which is equal to 1024. Therefore, there are 1024 ways to set the switches for the garage door opener.