Question

Calculate the number of bit strings of length 5 or less.

Answer 1

Let $a_1a_2...a_n$ be a bit string of length $n$. So, $a_i$ can have two values for each $i\in\{1,2,...,n\}$. Then by Multiplication Principle the number of bit string of length $n$ is $2\cdot2\cdot ...\cdot 2=2^n$.

Consequently,  the number of bit strings of length 5 or less is equal to

$2+2^2+2^3+2^4+2^5=2+4+8+16+32=62.$

Answer: 62