  We use the convolution method for arithmetic functions of several variables
to deduce an asymptotic formula for the number of $k$-tuples of positive
integers with components which are pairwise non-coprime and $\le x$. More
generally, we obtain asymptotic formulas on the number of $k$-tuples
$(n_1,\ldots,n_k)\in {\Bbb N}^k$ such that at least $r$ pairs $(n_i,n_j)$,
respectively exactly $r$ pairs are coprime. Our results answer the questions
raised by Moree (2005, 2014), and generalize and refine related results
obtained by Heyman (2014) and Hu (2014).
