1.3.9 problem 38

(a)

There are $12$ choices of seats for Tyron and Cersei so that they sit next to each other ($11$ cases, where they take $i-1$ and $i$ positions and 1 case, where they take 1 and 12th position, because table is round). Tyron can sit to the left or to the right of Cersei. The remaining $10$ people can be ordered in $10!$ ways, so the answer is $$\frac{24\times 10!}{12!}=\frac{2}{11}$$

(b)

There are $\left(\frac{12}{2}\right)$ choices of seats to be assigned to Tyron and Cersei, but only $12$ choices where they sit next to each other. Since every assignment of seats is equally likely the answer is $$\frac{12}{\left(\frac{12}{2}\right)}=\frac{2}{11}$$