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Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?
- a)240
- b)480
- c)720
- d)1440
- e)3600
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Seven children — A, B, C, D, E, F, and G — are going to si...
Understanding the problem:
- Child A must sit next to both B and G.
- B and G must be adjacent to A.
- The other four children (C, D, E, F) can sit in any order in the remaining seats.
Solution:
- Since B and G must be seated next to A, we can think of them as a single unit BG.
- So, now we have 6 units (A, BG, C, D, E, F) to be seated in 6 chairs.
- The number of ways to arrange 6 units in 6 chairs is 6! = 720.
- However, within the BG unit, B and G can be arranged in 2 ways (BG or GB).
- So, the total number of possible configurations is 720 * 2 = 1440.
- But we need to consider that the order of the children within the BG unit does not matter.
- So, we need to divide 1440 by 2 (since we counted each arrangement twice).
- Therefore, the final answer is 1440 / 2 = 720 possible configurations.
Therefore, the correct answer is option A) 720.
- Child A must sit next to both B and G.
- B and G must be adjacent to A.
- The other four children (C, D, E, F) can sit in any order in the remaining seats.
Solution:
- Since B and G must be seated next to A, we can think of them as a single unit BG.
- So, now we have 6 units (A, BG, C, D, E, F) to be seated in 6 chairs.
- The number of ways to arrange 6 units in 6 chairs is 6! = 720.
- However, within the BG unit, B and G can be arranged in 2 ways (BG or GB).
- So, the total number of possible configurations is 720 * 2 = 1440.
- But we need to consider that the order of the children within the BG unit does not matter.
- So, we need to divide 1440 by 2 (since we counted each arrangement twice).
- Therefore, the final answer is 1440 / 2 = 720 possible configurations.
Therefore, the correct answer is option A) 720.
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Community Answer
Seven children — A, B, C, D, E, F, and G — are going to si...
To begin with, let's examine the restricted elements, namely children A, B, and G, who must be seated together in a consecutive arrangement of three seats. How many possible arrangements are there for these "three in a row" seats in a row of seven seats?
X X X _ _ _ _
_ X X X _ _ _
_ _ X X X _ _
_ _ _ X X X _
_ _ _ _ X X X
There are a total of five distinct locations where these three children can be seated in a consecutive manner. Now, for any specific group of three seats, we know that child A must occupy the middle seat, allowing for only two possible seating orders: B-A-G or G-A-B. Consequently, the total number of configurations for these three children is 5 multiplied by 2, resulting in 10.
Moving on to the non-restricted elements, which consist of the remaining four children. Once A, B, and G are seated, the remaining four children can be arranged in any order among the four remaining seats. This corresponds to a permutation of the four items, denoted as 4P4, which equals 4! and results in 24 possible arrangements. For each individual seating configuration of A, B, and G, there are 24 distinct ways in which the other children can be seated in the remaining seats.
Finally, let's combine the information using the Fundamental Counting Principle. We have 10 possible arrangements for the first three children and 24 possible arrangements for the remaining four. Multiplying these two numbers together gives us a total number of configurations of 24 multiplied by 10, which equals 240.
Therefore, the answer is 240.
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Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?a)240b)480c)720d)1440e)3600Correct answer is option 'A'. 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 Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?a)240b)480c)720d)1440e)3600Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?a)240b)480c)720d)1440e)3600Correct answer is option 'A'. Can you explain this answer?.
Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?a)240b)480c)720d)1440e)3600Correct answer is option 'A'. 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 Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?a)240b)480c)720d)1440e)3600Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?a)240b)480c)720d)1440e)3600Correct answer is option 'A'. Can you explain this answer?.
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Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?a)240b)480c)720d)1440e)3600Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?a)240b)480c)720d)1440e)3600Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?a)240b)480c)720d)1440e)3600Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?a)240b)480c)720d)1440e)3600Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.
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