Question

Number of positive integral solution of the equation $xyz=60$ is

• A. $54$
• B. $27$
• C. $81$
• D. None of these

Answer 1

Answer: (A)

$54$

$xyz=60$ can be made in following ways :
$1\times 12\times 53\times 4\times 52\times 6\times 51\times 6\times 102\times 3\times 101\times 4\times 151\times 3\times 201\times 2\times 32\times 2\times 151\times 1\times 60$
but we know that the triplets in these $8$ arrays can be attributed to any of $x$ or $y$ or $z$

The first $6$ can be distributed to all $x,y$ and $z$, whereas in the last $2$, there will be repetitions, so considering that, total number of solutions$=8\times 3!+2\times \frac{3!}{2}=54$
Hence, option $A$ is correct.