Class 11 Mathematics Permutations and Combinations Derivations of formulas and their connections Expert Level 64

\(x_1+x_2+x_3=15\) में \(0\leq x_i\leq6\) हो, तो inclusion-exclusion में कौन-सा expression सही है?

In \(x_1+x_2+x_3=15\) with \(0\leq x_i\leq6\), which expression is correct by inclusion-exclusion?

Explanation opens after your attempt
Correct Answer

A. \(^{17}C_2-3{}^{10}C_2+3{}^{3}C_2\)

Step 1

Concept

Cases with \(x_i\geq7\) are subtracted and double violations are added. In exams shift by (7) for bounded solutions.

Step 2

Why this answer is correct

The correct answer is A. \(^{17}C_2-3{}^{10}C_2+3{}^{3}C_2\). Cases with \(x_i\geq7\) are subtracted and double violations are added. In exams shift by (7) for bounded solutions.

Step 3

Exam Tip

Upper bound तोड़ने पर \(x_i\geq7\) के cases घटते और double violations जुड़ते हैं। परीक्षा में bounded solutions में (7) shift करें।

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\(x_1+x_2+x_3=15\) में \(0\leq x_i\leq6\) हो, तो inclusion-exclusion में कौन-सा expression सही है? / In \(x_1+x_2+x_3=15\) with \(0\leq x_i\leq6\), which expression is correct by inclusion-exclusion?

Correct Answer: A. \(^{17}C_2-3{}^{10}C_2+3{}^{3}C_2\). Explanation: Upper bound तोड़ने पर \(x_i\geq7\) के cases घटते और double violations जुड़ते हैं। परीक्षा में bounded solutions में (7) shift करें। / Cases with \(x_i\geq7\) are subtracted and double violations are added. In exams shift by (7) for bounded solutions.

Which concept should I revise for this Mathematics MCQ?

Cases with \(x_i\geq7\) are subtracted and double violations are added. In exams shift by (7) for bounded solutions.

What exam hint can help solve this Mathematics question?

Upper bound तोड़ने पर \(x_i\geq7\) के cases घटते और double violations जुड़ते हैं। परीक्षा में bounded solutions में (7) shift करें।