Question:
The total number of positive integral solutions $(x, y, z)$ such that $x y z=24$ is
Correct Option: , 4
Solution:
$x \cdot y \cdot z=24$
$x \cdot y \cdot z=2^{3} \cdot 3^{1}$
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