Question 14
The English alphabet, which has 26 letters, is randomly permuted. Let $p_{1}$ be the probability that $\mathrm{AB}$, $\mathrm{CD}$, and $EF$ all appear as contiguous substrings. Let $p_{2}$ be the probability that $ABC$ and $DEF$ both appear as contiguous substrings. Compute $\frac{p_{1}}{p_{2}}$.