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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
- a)240
- b)200
- c)120
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The number of ways in which 7 boys sit in a round table so that two pa...
The 2 boys can be arranged in 2 ways; they form a unit.
So now you have 6 units.
At a round table those 6 can be arranged is 5! ways.
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Total # of arrangements = 2*5! = 2*120 = 240 ways
Most Upvoted Answer
The number of ways in which 7 boys sit in a round table so that two pa...
Given: 7 boys and 2 particular boys
To calculate: Number of ways they can sit in a round table where 2 particular boys sit together
Solution:
Let's assume the two particular boys as a single entity (let's call it X) for now. So, we have 6 entities (5 boys + 1 X) to arrange in a round table. The number of ways to arrange n entities in a circular permutation is (n-1)!. Therefore, the number of ways to arrange 6 entities in a round table is 5!.
Now, let's consider the two particular boys as distinct entities (let's call them A and B). Since A and B can be arranged in two ways (AB or BA), we need to multiply the number of ways to arrange 5 entities with the number of ways to arrange A and B. Therefore, the total number of ways to arrange 7 boys in a round table so that A and B sit together is:
5! × 2 = 240
Therefore, option (A) is the correct answer.
To calculate: Number of ways they can sit in a round table where 2 particular boys sit together
Solution:
Let's assume the two particular boys as a single entity (let's call it X) for now. So, we have 6 entities (5 boys + 1 X) to arrange in a round table. The number of ways to arrange n entities in a circular permutation is (n-1)!. Therefore, the number of ways to arrange 6 entities in a round table is 5!.
Now, let's consider the two particular boys as distinct entities (let's call them A and B). Since A and B can be arranged in two ways (AB or BA), we need to multiply the number of ways to arrange 5 entities with the number of ways to arrange A and B. Therefore, the total number of ways to arrange 7 boys in a round table so that A and B sit together is:
5! × 2 = 240
Therefore, option (A) is the correct answer.
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Community Answer
The number of ways in which 7 boys sit in a round table so that two pa...
Take two boys as one one units i.e,1+1=2 units
(7-2)=5factorial again multiply with that 2 units × 5 factorial
5×4×3×2×1=120× 2 units=240
(7-2)=5factorial again multiply with that 2 units × 5 factorial
5×4×3×2×1=120× 2 units=240
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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 isa)240b)200c)120d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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