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The total number of positive integral solutions $(x, y, z)$ such that $xyz = 24$ is
(1) 36
(2) 45
(3) 24
(4) 30
$xyz = 24 = 2^3 \cdot 3^1$. Distribute prime factors among 3 persons. For $2^3$: ${}^5C_2 = 10$ ways. For $3^1$: ${}^3C_2 = 3$ ways. Total $= {}^5C_2 \cdot {}^3C_2 = 10 \times 3 = 30$.
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