JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of triplets \((x, y, z)\). where \(x, y, z\) are distinct non negative integers satisfying \(x+y+z=15\), is
- A \(80\)
- B \(114\)
- C \(92\)
- D \(136\)
Answer & Solution
Correct Answer
(B) \(114\)
Step-by-step Solution
Detailed explanation
\(x+y+z=15\) Total no. of solution \(={ }^{15+3-1} C _{3-1}=136\) Let \(x = y \neq z\) \(2 x + z =15 \Rightarrow z =15-2 t\) \(\Rightarrow r \in\{0,1,2, \ldots 7\}-\{5\}\) \(\therefore 7 \text { solutions }\) \(\therefore 7\) solutions \(\therefore\) there are 21 solutions in…
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