The total number of positive

$x \cdot y \cdot z=24$

$x \cdot y \cdot z=2^{3} \cdot 3^{1}$

Now using beggars method. 3 things to be distributed among 3 persons\

Each may receive none, one or more $\therefore{ }^{5} \mathrm{C}_{2}$ ways

Similarly for $1^{\prime} \therefore{ }^{3} \mathrm{C}_{2}$ ways

Total ways $={ }^{5} \mathrm{C}_{2} \cdot{ }^{3} \mathrm{C}_{2}=30$ ways