Class 11 Mathematics - Permutations And Combinations - Derivations of formulas and their connections Expert Quiz

Mathematics Permutations And Combinations Derivations of formulas and their connections Expert Class 11 Level 58

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Question 1/2 Expert Mathematics Permutations and Combinations Permutations Class 11 Level 58

शब्द (PERMUTATION) की व्यवस्थाओं में व्यंजन अपने मूल सापेक्ष क्रम में रहें, ऐसी कितनी व्यवस्थाएं होंगी?

In arrangements of (PERMUTATION), how many have the consonants in their original relative order?

Explanation opens after your attempt
Correct Answer

B. (55440)

Step 1

Concept

Choose consonant positions in \(^{11}C_6\) ways and arrange the (5) vowels in (5!) ways. When relative order is fixed, only positions are chosen.

Step 2

Why this answer is correct

The correct answer is B. (55440). Choose consonant positions in \(^{11}C_6\) ways and arrange the (5) vowels in (5!) ways. When relative order is fixed, only positions are chosen.

Step 3

Exam Tip

व्यंजनों के स्थान \(^{11}C_6\) तरीकों से चुनें और शेष (5) स्वरों को (5!) तरीकों से रखें। सापेक्ष क्रम निश्चित हो तो केवल स्थान चुनने होते हैं।

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Question 2/2 Expert Mathematics Permutations and Combinations Permutations Class 11 Level 58

(8) व्यक्तियों को (8) अलग कार्य दिए जाते हैं। यदि ठीक (2) व्यक्तियों को अपना सही कार्य मिले, तो कितने वितरण संभव हैं?

(8) people are assigned (8) distinct jobs. If exactly (2) people get their correct jobs, how many assignments are possible?

Explanation opens after your attempt
Correct Answer

C. (7420)

Step 1

Concept

Choose the (2) correctly assigned people in \(^{8}C_2\) ways and derange the remaining (6) with \(D_6=265\). Exactly (2) correct means all others are wrong.

Step 2

Why this answer is correct

The correct answer is C. (7420). Choose the (2) correctly assigned people in \(^{8}C_2\) ways and derange the remaining (6) with \(D_6=265\). Exactly (2) correct means all others are wrong.

Step 3

Exam Tip

सही कार्य पाने वाले \(^{8}C_2\) तरीकों से चुनें और बाकी (6) का विस्थापन \(D_6=265\) है। ठीक (2) सही का मतलब बाकी सभी गलत होंगे।

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