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

(6) boys और (5) girls को row में बैठाना है ताकि कोई दो girls साथ न बैठें। Girls placement factor क्या होगा?

(6) boys and (5) girls are seated in a row so that no two girls sit together. What is the girls placement factor?

Explanation opens after your attempt
Correct Answer

B. \(^{7}C_5\cdot5!\)

Step 1

Concept

After (6) boys, (7) gaps are formed, and (5) girls are arranged in them. In exams use the gap method for no two together.

Step 2

Why this answer is correct

The correct answer is B. \(^{7}C_5\cdot5!\). After (6) boys, (7) gaps are formed, and (5) girls are arranged in them. In exams use the gap method for no two together.

Step 3

Exam Tip

(6) boys के बाद (7) gaps बनते हैं, जिनमें (5) girls arrange होती हैं। परीक्षा में no two together में gap method लगाएं।

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Question Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(5) vowels और (7) consonants से word बनाना है जिसमें no two vowels together हों। Vowel placement का factor क्या होगा?

A word is formed from (5) vowels and (7) consonants with no two vowels together. What is the vowel placement factor?

Explanation opens after your attempt
Correct Answer

A. \(^{8}C_5\cdot5!\)

Step 1

Concept

After arranging (7) consonants, (8) gaps are formed and (5) vowels are arranged. In exams choose gaps and permute vowels.

Step 2

Why this answer is correct

The correct answer is A. \(^{8}C_5\cdot5!\). After arranging (7) consonants, (8) gaps are formed and (5) vowels are arranged. In exams choose gaps and permute vowels.

Step 3

Exam Tip

(7) consonants के arrangement के बाद (8) gaps बनते हैं और (5) vowels arrange होते हैं। परीक्षा में gaps चुनकर vowels permute करें।

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Question Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(6) boys और (4) girls को row में arrange करना है ताकि no two girls together हों। Derivation का मुख्य step क्या है?

Arrange (6) boys and (4) girls in a row so that no two girls are together. What is the main step in the derivation?

Explanation opens after your attempt
Correct Answer

B. पहले boys arrange करें और फिर (7) gaps में (4) girls रखेंArrange boys first and place (4) girls in (7) gaps

Step 1

Concept

Arranging boys creates (7) gaps where girls can be placed. In exams use the gap method for no two together.

Step 2

Why this answer is correct

The correct answer is B. पहले boys arrange करें और फिर (7) gaps में (4) girls रखें / Arrange boys first and place (4) girls in (7) gaps. Arranging boys creates (7) gaps where girls can be placed. In exams use the gap method for no two together.

Step 3

Exam Tip

Boys arrange करने पर (7) gaps बनते हैं जिनमें girls बैठती हैं। परीक्षा में no two together के लिए gap method लगाएं।

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Question Expert Mathematics Permutations and Combinations Combinations Class 11 Level 62

(1) से (15) तक की संख्याओं में से (5) संख्याएं चुननी हैं, जिनमें कोई दो लगातार न हों। कितने तरीके हैं?

Choose (5) numbers from (1) to (15) such that no two are consecutive. How many ways are possible?

Explanation opens after your attempt
Correct Answer

A. (462)

Step 1

Concept

By the gap method, the count is \(^{15-5+1}C_{5}=^{11}C_{5}=462\). In such problems identify the gap condition first.

Step 2

Why this answer is correct

The correct answer is A. (462). By the gap method, the count is \(^{15-5+1}C_{5}=^{11}C_{5}=462\). In such problems identify the gap condition first.

Step 3

Exam Tip

अलगाव विधि से संख्या \(^{15-5+1}C_{5}=^{11}C_{5}=462\)। ऐसी समस्याओं में पहले अंतर की शर्त पहचानें।

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Question Expert Mathematics Permutations and Combinations Fundamental principle of counting Class 11 Level 52

लंबाई (7) की कितनी द्विआधारी श्रेणियाँ बनेंगी जिनमें ठीक (4) शून्य हों और लगातार (3) शून्य कहीं न आएँ?

How many binary strings of length (7) have exactly (4) zeros and no occurrence of (3) consecutive zeros?

Explanation opens after your attempt
Correct Answer

C. (19)

Step 1

Concept

Place the (4) zeros in the (4) gaps around the (3) ones, with no gap receiving more than (2) zeros. Control forbidden consecutiveness by gap limits.

Step 2

Why this answer is correct

The correct answer is C. (19). Place the (4) zeros in the (4) gaps around the (3) ones, with no gap receiving more than (2) zeros. Control forbidden consecutiveness by gap limits.

Step 3

Exam Tip

(3) एकों के आसपास बने (4) खाली स्थानों में (4) शून्य रखें और किसी स्थान पर (2) से अधिक शून्य न रखें। प्रतिबंधित लगातारपन को खाली स्थान सीमा से नियंत्रित करें।

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Question Expert Mathematics Permutations and Combinations Fundamental principle of counting Class 11 Level 52

(6) पुरुष और (4) महिलाएँ गोल मेज पर बैठते हैं। कोई दो महिलाएँ साथ-साथ न बैठें। कुल कितनी व्यवस्थाएँ होंगी?

(6) men and (4) women sit around a round table. No two women should sit together. How many arrangements are possible?

Explanation opens after your attempt
Correct Answer

C. (43200)

Step 1

Concept

First seat the men around the circle in ((6-1)!) ways and place the (4) women in the (6) gaps. Use the gap method for circular separation.

Step 2

Why this answer is correct

The correct answer is C. (43200). First seat the men around the circle in ((6-1)!) ways and place the (4) women in the (6) gaps. Use the gap method for circular separation.

Step 3

Exam Tip

पहले पुरुषों को वृत्त में ((6-1)!) तरीकों से बैठाएँ और उनके (6) खाली स्थानों में (4) महिलाओं को रखें। वृत्तीय अलगाव में खाली स्थान विधि प्रयोग करें।

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Question Expert Mathematics Permutations and Combinations Fundamental principle of counting Class 11 Level 52

शब्द (BANANA) के अक्षरों से कितने भिन्न क्रम बनेंगे जिनमें कोई दो (A) साथ-साथ न हों?

How many distinct arrangements of the letters of (BANANA) are possible if no two (A)'s are adjacent?

Explanation opens after your attempt
Correct Answer

C. (12)

Step 1

Concept

First arrange (B,N,N), then place the (3) identical (A)'s in the (4) gaps formed. Handle repeated letters and gaps carefully.

Step 2

Why this answer is correct

The correct answer is C. (12). First arrange (B,N,N), then place the (3) identical (A)'s in the (4) gaps formed. Handle repeated letters and gaps carefully.

Step 3

Exam Tip

पहले (B,N,N) को सजाएँ और बने (4) खाली स्थानों में (3) समान (A) रखें। समान अक्षरों और खाली स्थानों को ध्यान से संभालें।

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Question Expert Mathematics Permutations and Combinations Fundamental principle of counting Class 11 Level 52

शब्द (STATISTICS) के अक्षरों से कितने भिन्न क्रम बनेंगे जिनमें कोई दो स्वर साथ-साथ न हों?

How many distinct arrangements of the letters of (STATISTICS) are possible if no two vowels are adjacent?

Explanation opens after your attempt
Correct Answer

C. (23520)

Step 1

Concept

First arrange the consonants and place vowels in the gaps formed. Do not forget division due to repeated letters.

Step 2

Why this answer is correct

The correct answer is C. (23520). First arrange the consonants and place vowels in the gaps formed. Do not forget division due to repeated letters.

Step 3

Exam Tip

पहले व्यंजनों को सजाकर बने खाली स्थानों में स्वरों को रखें। समान अक्षरों के कारण विभाजन करना न भूलें।

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Question Hard Mathematics Permutations and Combinations Fundamental principle of counting Class 11 Level 54

(4) अलग गणित और (3) अलग अंग्रेजी की पुस्तकों को पंक्ति में सजाना है। कोई भी दो अंग्रेजी पुस्तकें साथ न हों। कुल व्यवस्थाएँ कितनी होंगी?

(4) distinct mathematics books and (3) distinct English books are to be arranged in a row. No two English books should be together. How many arrangements are possible?

Explanation opens after your attempt
Correct Answer

B. (1440)

Step 1

Concept

First arrange the mathematics books in (4!) ways, then place the (3) English books in (5) gaps with order. The gap method is useful for separation restrictions.

Step 2

Why this answer is correct

The correct answer is B. (1440). First arrange the mathematics books in (4!) ways, then place the (3) English books in (5) gaps with order. The gap method is useful for separation restrictions.

Step 3

Exam Tip

पहले गणित की पुस्तकें (4!) तरीकों से रखें और बने (5) खाली स्थानों में (3) अंग्रेजी पुस्तकें क्रम सहित रखें। अलग-अलग रखने में खाली स्थान विधि उपयोगी है।

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