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The number of ways in which 7 boys sit in a round table so that two particular boys may sit together is?
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The number of ways in which 7 boys sit in a round table so that two pa...
Understanding the Problem
To find the number of ways in which 7 boys can sit at a round table with the condition that two particular boys must sit together, we can treat the two boys as a single unit or block.
Forming a Block
1. Two Boys as One Unit:
- Treat the two specific boys (let's call them A and B) as a single block. This reduces the problem to arranging 6 units (the block and the other 5 boys).
Arranging the Units
2. Arranging 6 Units in a Circle:
- The number of ways to arrange n people around a circular table is (n-1)!. Hence, for our 6 units:
- Arrangements = (6 - 1)! = 5! = 120 ways.
Arranging the Boys Within the Block
3. Arranging the Two Boys:
- Within their block, the two boys A and B can be arranged in 2 ways (A next to B or B next to A).
Calculating Total Arrangements
4. Total Arrangements:
- Therefore, the total number of arrangements is:
- Total = Arrangements of 6 units × Arrangements of A and B = 120 × 2 = 240 ways.
Conclusion
Thus, the total number of ways in which 7 boys can sit at a round table, ensuring that two particular boys sit together, is 240 ways.
To find the number of ways in which 7 boys can sit at a round table with the condition that two particular boys must sit together, we can treat the two boys as a single unit or block.
Forming a Block
1. Two Boys as One Unit:
- Treat the two specific boys (let's call them A and B) as a single block. This reduces the problem to arranging 6 units (the block and the other 5 boys).
Arranging the Units
2. Arranging 6 Units in a Circle:
- The number of ways to arrange n people around a circular table is (n-1)!. Hence, for our 6 units:
- Arrangements = (6 - 1)! = 5! = 120 ways.
Arranging the Boys Within the Block
3. Arranging the Two Boys:
- Within their block, the two boys A and B can be arranged in 2 ways (A next to B or B next to A).
Calculating Total Arrangements
4. Total Arrangements:
- Therefore, the total number of arrangements is:
- Total = Arrangements of 6 units × Arrangements of A and B = 120 × 2 = 240 ways.
Conclusion
Thus, the total number of ways in which 7 boys can sit at a round table, ensuring that two particular boys sit together, is 240 ways.
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The number of ways in which 7 boys sit in a round table so that two particular boys may sit together is?
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The number of ways in which 7 boys sit in a round table so that two particular boys may sit together is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of ways in which 7 boys sit in a round table so that two particular boys may sit together is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of ways in which 7 boys sit in a round table so that two particular boys may sit together is?.
The number of ways in which 7 boys sit in a round table so that two particular boys may sit together is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of ways in which 7 boys sit in a round table so that two particular boys may sit together is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of ways in which 7 boys sit in a round table so that two particular boys may sit together is?.
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