Lecture 1, Problem 1.28

I got $26 \cdot 25^6-16 \cdot 25^5$, but the answer says that it's $26 \cdot 25^6-21 \cdot 20 \cdot 25^5$. The list of consonants is: b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z. The pairs of consecutive consonants are: (b, c), (c, d), (f, g), (g, h), (j, k), (k, l), (l, m), (m, n), (p, q), (q, r), (r, s), (s, t), (v, w), (w, x), (x, y), (y, z). There are 16 pairs, so the second part is $16 \cdot 25^5$. The first part is $26 \cdot 25^6$.