KöMaL 2023 C1752

There are six people waiting in a line. It is taking very long, so they decide to play. They select a permutation of the six positions at random, and perform it three times successively. (A permutation is a rule of obtaining a new order by assigning a (possibly) new position to everyone. For example they may chose the following rule: the person at position 1 goes to position 3, the one at position 2 goes to position 1, the third goes to position 2, the fourth goes to position 6, the fifth stays in place, and the sixth goes to position 4.) What is the probability that at least one of them will be standing in their initial position at the end?