11.75 (1990)

Let us consider the class of groups with $n$ generators and $m$ relators. A subclass of this class is called dense if the ratio of the number of presentations of the form $\langle a_1, \dots, a_n \mid R_1, \dots, R_m \rangle$ (where $|R_i| = d_i$) for groups from this subclass to the number of all such presentations converges to 1 when $d_1 + \dots + d_m$ tends to infinity. Prove that for every $k < m$ and for any $n$ the subclass of groups all of whose $k$-generator subgroups are free is dense.