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  4. The number of integral solution(s) of the equation xyz = 360 is 180 m, then m equals

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Q. The number of integral solution(s) of the equation $xyz = 360$ is $180\, m$, then m equals

Permutations and Combinations

Solution:

$xyz = 360$
$x y z=2^3 \times 3^2 \times 5$
Number of natural solutions are ${ }^5 C _2 \times{ }^4 C _2 \times{ }^3 C _2=180$
Number of integral solutions are $=4 \times 180$
$\Rightarrow m =4$.