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

(n) people को (n) seats पर इस तरह बैठाना कि exactly (k) people सही seats पर हों, count क्या है?

What is the count for seating (n) people in (n) seats so that exactly (k) people are in their correct seats?

Explanation opens after your attempt
Correct Answer

A. \(^{n}C_kD_{n-k}\)

Step 1

Concept

First choose the (k) correctly seated people, then derange the remaining (n-k). In exams use choose fixed plus derange rest for exactly fixed points.

Step 2

Why this answer is correct

The correct answer is A. \(^{n}C_kD_{n-k}\). First choose the (k) correctly seated people, then derange the remaining (n-k). In exams use choose fixed plus derange rest for exactly fixed points.

Step 3

Exam Tip

पहले सही बैठे (k) people चुनें, फिर बाकी (n-k) का derangement करें। परीक्षा में exactly fixed points के लिए choose fixed plus derange rest करें।

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(n) people को (n) seats पर इस तरह बैठाना कि exactly (k) people सही seats पर हों, count क्या है? / What is the count for seating (n) people in (n) seats so that exactly (k) people are in their correct seats?

Correct Answer: A. \(^{n}C_kD_{n-k}\). Explanation: पहले सही बैठे (k) people चुनें, फिर बाकी (n-k) का derangement करें। परीक्षा में exactly fixed points के लिए choose fixed plus derange rest करें। / First choose the (k) correctly seated people, then derange the remaining (n-k). In exams use choose fixed plus derange rest for exactly fixed points.

Which concept should I revise for this Mathematics MCQ?

First choose the (k) correctly seated people, then derange the remaining (n-k). In exams use choose fixed plus derange rest for exactly fixed points.

What exam hint can help solve this Mathematics question?

पहले सही बैठे (k) people चुनें, फिर बाकी (n-k) का derangement करें। परीक्षा में exactly fixed points के लिए choose fixed plus derange rest करें।