Question

The total number of positive integral solutions of $abc=30$ is

• A. $30$
• B. $27$
• C. $8$
• D. None of these

Answer 1

Answer: (B)

$27$

Number of the integral solution for $abc=30$ are:

$1\times 3\times 10\Rightarrow \text{Permutation}=3!15\times 2\times 1\Rightarrow \text{Permutation}=3!5\times 3\times 2\Rightarrow \text{Permutation}=3!5\times 6\times 1\Rightarrow \text{Permutation}=3!30\times 1\times 1\Rightarrow \text{Permutation}=\frac{3!}{2!}$

Total solutions $=(3!\times 4)+3=27$