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A club with x members is organized into tour committees such that
(a) each member is in exactly two committees,
(b) any two committees have exactly one member in common.
(b) any two committees have exactly one member in common.
Then x has
- a)exactly two values both between 4 and 8
- b)exactly one value and this lies between 4 and 8
- c)exactly two values both between 8 and 16
- d)exactly one value and this lies between 8 and 16.
Correct answer is option 'B'. Can you explain this answer?
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A club with x members is organized into tour committees such that(a)ea...
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A club with x members is organized into tour committees such that(a)ea...
My thought is option BB and x=6x=6. Please somebody tell me am I right or wrong?
Let the committees be A1,A2,A3,A4A1,A2,A3,A4 then |A1∪A2∪A3∪A4|=n|A1∪A2∪A3∪A4|=n. There are (42)=6(42)=6 pairwise intersections each of size 11and each intersection of triples must be empty since if not some member would belong to 33committees, a contradiction. If we make a 4×n4×n table where rows are committees and columns are members and mark a 11 whenever member xjxj belongs to committee AiAi we notice that the ithith row sum is |Ai||Ai| and the jthjthcolumn sum is 22 (since each member belongs to exactly 22 committees) so equating row and column sums we get ∑4i=1|Ai|=2n.∑i=14|Ai|=2n.
Putting this information together and using the inclusion-exclusion formula we get n=6
Let the committees be A1,A2,A3,A4A1,A2,A3,A4 then |A1∪A2∪A3∪A4|=n|A1∪A2∪A3∪A4|=n. There are (42)=6(42)=6 pairwise intersections each of size 11and each intersection of triples must be empty since if not some member would belong to 33committees, a contradiction. If we make a 4×n4×n table where rows are committees and columns are members and mark a 11 whenever member xjxj belongs to committee AiAi we notice that the ithith row sum is |Ai||Ai| and the jthjthcolumn sum is 22 (since each member belongs to exactly 22 committees) so equating row and column sums we get ∑4i=1|Ai|=2n.∑i=14|Ai|=2n.
Putting this information together and using the inclusion-exclusion formula we get n=6
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A club with x members is organized into tour committees such that(a)ea...
Explanation:
Given Conditions:
- Each member is in exactly two committees.
- Any two committees have exactly one member in common.
Reasoning:
- Let's assume there are 'x' members in the club.
- Each member is in exactly two committees, which means there are a total of 2x committee memberships.
- Since any two committees have exactly one member in common, each member is counted twice in the total committee memberships.
- Therefore, the total committee memberships must equal 2x.
Analysis:
- The total number of committee memberships is equal to the sum of the sizes of all committees.
- Let's denote the size of each committee as 'y'.
- The total number of committee memberships is also equal to the total number of committee-member pairs, which is x*y.
- Therefore, 2x = x*y.
Conclusion:
- Solving the equation 2x = x*y gives us y = 2.
- This implies that each committee has 2 members.
- Since each member is in exactly two committees, the total number of members x must be even.
- The only even number between 4 and 8 is 4, so the only possible value for x is 4.
- Hence, the correct answer is that x has exactly one value between 4 and 8.
Given Conditions:
- Each member is in exactly two committees.
- Any two committees have exactly one member in common.
Reasoning:
- Let's assume there are 'x' members in the club.
- Each member is in exactly two committees, which means there are a total of 2x committee memberships.
- Since any two committees have exactly one member in common, each member is counted twice in the total committee memberships.
- Therefore, the total committee memberships must equal 2x.
Analysis:
- The total number of committee memberships is equal to the sum of the sizes of all committees.
- Let's denote the size of each committee as 'y'.
- The total number of committee memberships is also equal to the total number of committee-member pairs, which is x*y.
- Therefore, 2x = x*y.
Conclusion:
- Solving the equation 2x = x*y gives us y = 2.
- This implies that each committee has 2 members.
- Since each member is in exactly two committees, the total number of members x must be even.
- The only even number between 4 and 8 is 4, so the only possible value for x is 4.
- Hence, the correct answer is that x has exactly one value between 4 and 8.
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A club with x members is organized into tour committees such that(a)each member is in exactly two committees,(b)any two committees have exactly one member in common.Then x hasa)exactly two values both between 4 and 8b)exactly one value and this lies between 4 and 8c)exactly two values both between 8 and 16d)exactly one value and this lies between 8 and 16.Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A club with x members is organized into tour committees such that(a)each member is in exactly two committees,(b)any two committees have exactly one member in common.Then x hasa)exactly two values both between 4 and 8b)exactly one value and this lies between 4 and 8c)exactly two values both between 8 and 16d)exactly one value and this lies between 8 and 16.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A club with x members is organized into tour committees such that(a)each member is in exactly two committees,(b)any two committees have exactly one member in common.Then x hasa)exactly two values both between 4 and 8b)exactly one value and this lies between 4 and 8c)exactly two values both between 8 and 16d)exactly one value and this lies between 8 and 16.Correct answer is option 'B'. Can you explain this answer?.
A club with x members is organized into tour committees such that(a)each member is in exactly two committees,(b)any two committees have exactly one member in common.Then x hasa)exactly two values both between 4 and 8b)exactly one value and this lies between 4 and 8c)exactly two values both between 8 and 16d)exactly one value and this lies between 8 and 16.Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A club with x members is organized into tour committees such that(a)each member is in exactly two committees,(b)any two committees have exactly one member in common.Then x hasa)exactly two values both between 4 and 8b)exactly one value and this lies between 4 and 8c)exactly two values both between 8 and 16d)exactly one value and this lies between 8 and 16.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A club with x members is organized into tour committees such that(a)each member is in exactly two committees,(b)any two committees have exactly one member in common.Then x hasa)exactly two values both between 4 and 8b)exactly one value and this lies between 4 and 8c)exactly two values both between 8 and 16d)exactly one value and this lies between 8 and 16.Correct answer is option 'B'. Can you explain this answer?.
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A club with x members is organized into tour committees such that(a)each member is in exactly two committees,(b)any two committees have exactly one member in common.Then x hasa)exactly two values both between 4 and 8b)exactly one value and this lies between 4 and 8c)exactly two values both between 8 and 16d)exactly one value and this lies between 8 and 16.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A club with x members is organized into tour committees such that(a)each member is in exactly two committees,(b)any two committees have exactly one member in common.Then x hasa)exactly two values both between 4 and 8b)exactly one value and this lies between 4 and 8c)exactly two values both between 8 and 16d)exactly one value and this lies between 8 and 16.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A club with x members is organized into tour committees such that(a)each member is in exactly two committees,(b)any two committees have exactly one member in common.Then x hasa)exactly two values both between 4 and 8b)exactly one value and this lies between 4 and 8c)exactly two values both between 8 and 16d)exactly one value and this lies between 8 and 16.Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A club with x members is organized into tour committees such that(a)each member is in exactly two committees,(b)any two committees have exactly one member in common.Then x hasa)exactly two values both between 4 and 8b)exactly one value and this lies between 4 and 8c)exactly two values both between 8 and 16d)exactly one value and this lies between 8 and 16.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
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