We saw in Section 1.2 that the answer to both these questions is \(2^9\text{,}\) as we can say yes or no (or 0 or 1) to each of the 9 elements in the set (positions in the bit-string). But \(2^9\) also looks like the answer you get from counting functions. In fact, if you count all functions \(f: A \to B\) with \(|A| = 9\) and \(|B| = 2\text{,}\) this is exactly what you get.
in-context