Constraint programming provides generic techniques to efficiently solve combinatorial problems. In this paper, we tackle the natural question of using constraint solvers to sample combinatorial problems in a generic way. We propose an algorithm, inspired from Meel's ApproxMC algorithm on SAT, to add hashing constraints to a CP model in order to split the search space into small cells. By uniformly sampling the solutions in one cell, we can generate random solutions without revamping the model of the problem. We ensure the randomness by introducing a new family of hashing constraints: randomly generated tables, which keeps the cost of the hashing process tractable. We implemented this solving method using the constraint solver Choco-solver. The quality of the randomness and the running time of our approach are experimentally compared to a random branching strategy. We show that our approach improves the randomness while being in the same order of magnitude in terms of running time. We also use our algorithm with an other, more powerful, set of hashing constraints: linear modular equalities. We experimentally show that the resulting sampling is uniform, at the cost of a longer running time.