This paper defines a selection problem which selects an appropriate object from a set that is specified by parameters. We discuss inductive learning of selection problems and give a method combining inductive logic programming (ILP) and Bayesian learning. It induces a binary relation comparing likelihood of objects being selected. Our methods estimate probability of each choice by evaluating variance of an induced relation from an ideal binary relation. Bayesian learning combines a prior probability of objects and the estimated probability. By making several assumptions on probability estimation, we give several methods. The methods are applied to Part-of-Speech tagging.