Find the total number of positive integr...

Find the total number of positive integral solutions for `(x ,y ,z)` such that `x y z=24.` Also find out the total number of integral solutions.

Verified by Experts

`becausexyz=24=2^(3)xx3^(1)`
Hence,, total number of positive integral solutions
`=(.^(3+3-1)C_(3-1))(.^(1+3-1)C_(3-1))`
`=.^(5)C_(2)xx.^(3)C_(2)=30`

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