2. [5] The English alphabet, which has 26 letters, is randomly permuted. Let $p_{1}$ be the probability that $\mathrm{AB}, \mathrm{CD}$, and $\mathrm{EF}$ all appear as contiguous substrings. Let $p_{2}$ be the probability that $\mathrm{ABC}$ and $\mathrm{DEF}$ both appear as contiguous substrings. Compute $\frac{p_{1}}{p_{2}}$.
Answer: $\square$
Solution: There are 23! ways to arrange the alphabet such that AB, CD, and EF all appear as contiguous substrings: treat each of these pairs of letters as a single merged symbol, which leaves 23 symbols to permute. Similarly, there are 22! ways to arrange the alphabet such that ABC and DEF both appear as contiguous substrings. Thus, $p_{1}=23!/ 26$ ! and $p_{2}=22!/ 26$ !, so the answer is $23!/ 22!=23$.