Class 11 Mathematics Permutations and Combinations Derivations of formulas and their connections Expert Level 66

\(x_1+x_2+x_3+x_4=22\) में \(x_1\geq1\), \(x_2\geq2\), \(x_3\geq3\), \(x_4\geq4\) हो, तो count क्या है?

In \(x_1+x_2+x_3+x_4=22\), if \(x_1\geq1\), \(x_2\geq2\), \(x_3\geq3\), \(x_4\geq4\), what is the count?

Explanation opens after your attempt
Correct Answer

B. \(^{15}C_3\)

Step 1

Concept

After removing the minimum sum (10), (12) remains and is distributed among (4) variables. In exams subtract lower bounds and use stars and bars.

Step 2

Why this answer is correct

The correct answer is B. \(^{15}C_3\). After removing the minimum sum (10), (12) remains and is distributed among (4) variables. In exams subtract lower bounds and use stars and bars.

Step 3

Exam Tip

Minimum sum (10) हटाने पर (12) बचता है और (4) variables में distribute होता है। परीक्षा में lower bounds subtract करके stars and bars लगाएं।

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\(x_1+x_2+x_3+x_4=22\) में \(x_1\geq1\), \(x_2\geq2\), \(x_3\geq3\), \(x_4\geq4\) हो, तो count क्या है? / In \(x_1+x_2+x_3+x_4=22\), if \(x_1\geq1\), \(x_2\geq2\), \(x_3\geq3\), \(x_4\geq4\), what is the count?

Correct Answer: B. \(^{15}C_3\). Explanation: Minimum sum (10) हटाने पर (12) बचता है और (4) variables में distribute होता है। परीक्षा में lower bounds subtract करके stars and bars लगाएं। / After removing the minimum sum (10), (12) remains and is distributed among (4) variables. In exams subtract lower bounds and use stars and bars.

Which concept should I revise for this Mathematics MCQ?

After removing the minimum sum (10), (12) remains and is distributed among (4) variables. In exams subtract lower bounds and use stars and bars.

What exam hint can help solve this Mathematics question?

Minimum sum (10) हटाने पर (12) बचता है और (4) variables में distribute होता है। परीक्षा में lower bounds subtract करके stars and bars लगाएं।