Task planning for robots is computationally challenging due to the combinatorial complexity of the possible action space. This fact is amplified if there are several subgoals to be achieved due to the increased length of the action sequences. In this work, we propose a multi-goal task planning algorithm for deterministic decision processes based on Monte Carlo Tree Search. We augment the algorithm by prioritized node expansion which prioritizes nodes that already have fulfilled some sub-goals. Due to its linear complexity in the number of sub-goals our algorithm is able to identify action sequences of 145 elements to reach the desired goal state with up to 48 sub-goals while the search tree is limited to under 6500 nodes. We use action reduction based on a kinematic reachability criterion to further ease computational complexity. We combine our algorithm with object localization and motion planning and apply it to a real-robot demonstration with two manipulators in an industrial bearing inspection setting.