Chapter 2 - Section 2-1 - Sample Spaces and Events - Exercises - Page 28: 2-34

4096

Every switch has 2 options, up and down. So, each switch can have two outcomes. There are 12 such switches, and there are $2 \times 2 \times ... \times 2=2^{12}$ possible outcomes. Therefore, there are $2^{12}=4096$ possible outcomes of the code.