AP EAMCET · Maths · Permutation Combination
The number of all possible positive integral solutions of the equation \(\mathrm{xyz}=30\) is
- A \(24\)
- B \(25\)
- C \(26\)
- D \(27\)
Answer & Solution
Correct Answer
(D) \(27\)
Step-by-step Solution
Detailed explanation
\(30 = 2^1 \cdot 3^1 \cdot 5^1\) \(\text{Number of solutions} = \binom{1+3-1}{3-1} \cdot \binom{1+3-1}{3-1} \cdot \binom{1+3-1}{3-1}\) \(= \binom{3}{2} \cdot \binom{3}{2} \cdot \binom{3}{2}\) \(= 3 \cdot 3 \cdot 3 = 27\)
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