Tidy-up tasks by service robots in home environments are challenging in robotics applications because they involve various interactions with the environment. In particular, robots are required not only to grasp, move, and release various home objects but also to plan the order and positions for placing the objects. In this paper, we propose a novel planning method that can efficiently estimate the order and positions of the objects to be tidied up by learning the parameters of a probabilistic generative model. The model allows a robot to learn the distributions of the co-occurrence probability of the objects and places to tidy up using the multimodal sensor information collected in a tidied environment. Additionally, we develop an autonomous robotic system to perform the tidy-up operation. We evaluate the effectiveness of the proposed method by an experimental simulation that reproduces the conditions of the Tidy Up Here task of the World Robot Summit 2018 international robotics competition. The simulation results show that the proposed method enables the robot to successively tidy up several objects and achieves the best task score among the considered baseline tidy-up methods.