How many bit strings have length 3, 4, or 5?

By the product rule there are:

• \(2^3\) bit strings of length 3
• \(2^4\) bit strings of length 4
• \(2^5\) bit strings of length 5

and by the sum rule we need to add them together to get the final result:

\[2^3 + 2^4 + 2^5 = 56\]