2012 Cayley Problem 22

Five monkeys are seated around a table. Their seats are labelled P, Q, R, S, and T, in clockwise order, as shown. The five monkeys are randomly numbered Monkey 1, Monkey 2, Monkey 3, Monkey 4, and Monkey 5. Monkey 1 remains in its seat. The remaining four monkeys then sit themselves in the remaining seats so that they are seated in clockwise order as Monkey 1, Monkey 2, Monkey 3, Monkey 4, and Monkey 5. What is the probability that the Monkey originally in seat R moves to seat P?

\textbf{(A)}\ \frac{1}{20}\quad \textbf{(B)}\ \frac{1}{10}\quad \textbf{(C)}\ \frac{3}{20}\quad \textbf{(D)}\ \frac{1}{5}\quad \textbf{(E)}\ \frac{1}{4}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.