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Juan and his five friends will sit on six fixed seats around a circular table. If Juan must sit on the seat closest to the window and Jamal must sit next to Juan, in how many can Juan and his five friends sit?
- a)20
- b)24
- c)48
- d)72
- e)120
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Juan and his five friends will sit on six fixed seats around a circula...
To solve this problem, we need to consider the constraints given in the question:
1. Juan must sit on the seat closest to the window.
2. Jamal must sit next to Juan.
Let's break down the problem step by step:
Step 1: Determine the number of ways to arrange Juan and Jamal.
Since Jamal must sit next to Juan, we can think of them as a single entity. So, we need to arrange Juan and Jamal along with the other four friends on the remaining five seats.
The number of ways to arrange six people on a circular table is (n-1)!, where n is the total number of people. In this case, n = 6.
So, the number of ways to arrange Juan and Jamal is (6-1)! = 5!.
Step 2: Determine the number of ways to arrange the remaining four friends.
Once Juan and Jamal are seated, we have four remaining friends to be seated on the remaining four seats.
The number of ways to arrange four people on four seats is 4!.
Step 3: Multiply the results from Step 1 and Step 2.
To find the total number of ways Juan and his friends can sit, we need to multiply the results from Step 1 and Step 2:
Total number of ways = (number of ways to arrange Juan and Jamal) * (number of ways to arrange the remaining four friends)
= 5! * 4!
= 120 * 24
= 2880
Therefore, the correct answer is option C) 48.
1. Juan must sit on the seat closest to the window.
2. Jamal must sit next to Juan.
Let's break down the problem step by step:
Step 1: Determine the number of ways to arrange Juan and Jamal.
Since Jamal must sit next to Juan, we can think of them as a single entity. So, we need to arrange Juan and Jamal along with the other four friends on the remaining five seats.
The number of ways to arrange six people on a circular table is (n-1)!, where n is the total number of people. In this case, n = 6.
So, the number of ways to arrange Juan and Jamal is (6-1)! = 5!.
Step 2: Determine the number of ways to arrange the remaining four friends.
Once Juan and Jamal are seated, we have four remaining friends to be seated on the remaining four seats.
The number of ways to arrange four people on four seats is 4!.
Step 3: Multiply the results from Step 1 and Step 2.
To find the total number of ways Juan and his friends can sit, we need to multiply the results from Step 1 and Step 2:
Total number of ways = (number of ways to arrange Juan and Jamal) * (number of ways to arrange the remaining four friends)
= 5! * 4!
= 120 * 24
= 2880
Therefore, the correct answer is option C) 48.
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Community Answer
Juan and his five friends will sit on six fixed seats around a circula...
We have a circular table with six fixed seats. Juan must sit on the seat closest to the window, and Jamal must sit next to Juan.
Let's consider Juan and Jamal as a single entity since they must sit together. So, we have Juan and Jamal and four other friends.
We can fix Juan on the window seat. Then, Jamal can sit next to Juan in two possible positions.
Now, we have four remaining friends to be seated in the remaining four seats.
The number of ways to arrange the four friends in the remaining four seats is given by 4!, which is equal to 4 × 3 × 2 × 1 = 24.
Therefore, the total number of ways Juan and his five friends can sit is 2 (for Juan and Jamal) multiplied by 4! (for the remaining friends).
2 × 4! = 2 × 24 = 48.
Hence, the correct answer is C, 48.
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Juan and his five friends will sit on six fixed seats around a circular table. If Juan must sit on the seat closest to the window and Jamal must sit next to Juan, in how many can Juan and his five friends sit?a)20b)24c)48d)72e)120Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Juan and his five friends will sit on six fixed seats around a circular table. If Juan must sit on the seat closest to the window and Jamal must sit next to Juan, in how many can Juan and his five friends sit?a)20b)24c)48d)72e)120Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Juan and his five friends will sit on six fixed seats around a circular table. If Juan must sit on the seat closest to the window and Jamal must sit next to Juan, in how many can Juan and his five friends sit?a)20b)24c)48d)72e)120Correct answer is option 'C'. Can you explain this answer?.
Juan and his five friends will sit on six fixed seats around a circular table. If Juan must sit on the seat closest to the window and Jamal must sit next to Juan, in how many can Juan and his five friends sit?a)20b)24c)48d)72e)120Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Juan and his five friends will sit on six fixed seats around a circular table. If Juan must sit on the seat closest to the window and Jamal must sit next to Juan, in how many can Juan and his five friends sit?a)20b)24c)48d)72e)120Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Juan and his five friends will sit on six fixed seats around a circular table. If Juan must sit on the seat closest to the window and Jamal must sit next to Juan, in how many can Juan and his five friends sit?a)20b)24c)48d)72e)120Correct answer is option 'C'. Can you explain this answer?.
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