TS EAMCET · Maths · Permutation Combination
The number of positive integral solutions of \(x y z=60\) is
- A \({ }^{59} \mathrm{C}_2\)
- B \({ }^4 \mathrm{C}_2 \times{ }^3 \mathrm{C}_2 \times{ }^3 \mathrm{C}_2\)
- C \({ }^4 \mathrm{C}_3\)
- D \({ }^3 \mathrm{C}_1 \times{ }^4 \mathrm{C}_0 \times{ }^4 \mathrm{C}_4\)
Answer & Solution
Correct Answer
(B) \({ }^4 \mathrm{C}_2 \times{ }^3 \mathrm{C}_2 \times{ }^3 \mathrm{C}_2\)
Step-by-step Solution
Detailed explanation
\(60 = 2^2 \cdot 3^1 \cdot 5^1\) For \(x y z = 2^2 \cdot 3^1 \cdot 5^1\), we have three separate equations for the exponents: \(a_1+a_2+a_3 = 2\) \(b_1+b_2+b_3 = 1\) \(c_1+c_2+c_3 = 1\) Number of solutions for exponents \((n=2, k=3)\) is \({}^{2+3-1} C_{3-1} = {}^4 C_2\). Number…
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