\(x_1+x_2+x_3+x_4=17\) में \(0\leq x_i\leq5\) हो, तो valid count कौन-सा है?
If \(x_1+x_2+x_3+x_4=17\) and \(0\leq x_i\leq5\), what is the valid count?
Explanation opens after your attempt
Correct Answer
A. \(^{20}C_3-4{}^{14}C_3+6{}^{8}C_3-4{}^{2}C_3\)
Concept
A violation starts at \(x_i\geq6\), so inclusion-exclusion applies. In exams use shift (6) for upper bound (5).
Why this answer is correct
The correct answer is A. \(^{20}C_3-4{}^{14}C_3+6{}^{8}C_3-4{}^{2}C_3\). A violation starts at \(x_i\geq6\), so inclusion-exclusion applies. In exams use shift (6) for upper bound (5).
Exam Tip
Violation \(x_i\geq6\) से शुरू होती है और inclusion-exclusion लागू होता है। परीक्षा में upper bound (5) हो तो shift (6) लें।
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