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The total number of positive integral solutions (x,y,z) such that xyz = 24 is

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answer is C.

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Detailed Solution

$x y z = 24 = 2^{3} \times 3^{1}$

$(\underline{x} \underline{y} \underline{z}) \Rightarrow r = 3 & n = 3, 1$

$∴$ no.of +ve integral sol’s

$^{(n + r - 1)} c_{r - 1} \times^{(n + r - 1)} c_{r - 1}$

$=^{5} c_{2} \times^{3} c_{2} = 10 (3) = 30$

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