We propose CABSC, a system that performs Constraint Acquisition Based on Solution Counting. In order to learn a Constraint Satisfaction Problem (CSP), the user provides positive examples and a Meta-CSP, i.e. a model of a combinatorial problem whose solution is a CSP. This Meta-CSP allows listing the potential constraints that can be part of the CSP the user wants to learn. It also allows stating the parameters of the constraints, such as the coefficients of a linear equation, and imposing constraints over these parameters. The CABSC reads the Meta-CSP using an augmented version of the language MiniZinc and returns the CSP that accepts the fewest solutions among the CSPs accepting all positive examples. This is done using a branch and bound where the bounding mechanism makes use of a model counter. Experiments show that CABSC is successful at learning constraints and their parameters from positive examples.