Suppose that a codeword of length 8 consists of letters \(A\), \(B\), or \(C\) or digits \(0\) or \(1\), and cannot start with \(1\). How many such codewords are there?

There are 4 choices for the first position (we’re excluding \(1\)) and \(5^7 = 78125\) choices for the subsequent positions for the total of:

\[4 \cdot 5^7 = 312500\]