43. Each day, one of n possible elements is requested, the ith one with probability Pi,i 1, n 1Pi = 1. These elements are at all times arranged in an ordered list which is revised as follows: The element selected is moved to the front of the list with the relative positions of all the other elements remaining unchanged. Define the state at any time to be the list ordering at that time and note that there are n! possible states.

(a) Argue that the preceding is a Markov chain.