The density of a subgroupoid with respect to a free groupoid is defined as the asymptotic ratio of their growths. This notion can be interpreted as a generalisation of the index's inverse for groups or as the probability of an element belonging to a subgroupoid. This more combinatorial strategy shows a richer picture of free groupoids than the bare algebraic perspective. We study the growth and density of several subgroupoids of a free groupoid. In addition, some aspects of enumeration related to the Motzkin paths are shown.