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In how many ways can 4 boys and 3 girls be seated in a row of 7 chairs if the boys and girls alternate?
- a)120
- b)140
- c)144
- d)288
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In how many ways can 4 boys and 3 girls be seated in a row of 7 chairs...
Approach:
To calculate the number of ways the boys and girls can be seated in a row of 7 chairs with the condition that they alternate, we can treat the boys and girls as separate groups and calculate the number of ways each group can be arranged.
Calculating the number of ways:
- Number of ways to arrange boys: There are 4 boys, so they can be arranged in 4! ways.
- Number of ways to arrange girls: There are 3 girls, so they can be arranged in 3! ways.
- Number of ways to arrange the combined group (boys and girls): Since boys and girls alternate, we can treat them as a single group of 7 people. This group can be arranged in 7! ways.
- Number of ways to arrange boys and girls alternately: To ensure boys and girls sit alternately, we multiply the number of ways to arrange boys and girls by the number of ways to arrange the combined group. So, the total number of ways = 4! * 3! * 7!
Calculating the total number of ways:
- 4! = 4 x 3 x 2 x 1 = 24
- 3! = 3 x 2 x 1 = 6
- 7! = 5040
- Total number of ways = 24 * 6 * 5040
- Total number of ways = 144 * 5040
- Total number of ways = 725760
Therefore, the correct answer is option C) 144.
To calculate the number of ways the boys and girls can be seated in a row of 7 chairs with the condition that they alternate, we can treat the boys and girls as separate groups and calculate the number of ways each group can be arranged.
Calculating the number of ways:
- Number of ways to arrange boys: There are 4 boys, so they can be arranged in 4! ways.
- Number of ways to arrange girls: There are 3 girls, so they can be arranged in 3! ways.
- Number of ways to arrange the combined group (boys and girls): Since boys and girls alternate, we can treat them as a single group of 7 people. This group can be arranged in 7! ways.
- Number of ways to arrange boys and girls alternately: To ensure boys and girls sit alternately, we multiply the number of ways to arrange boys and girls by the number of ways to arrange the combined group. So, the total number of ways = 4! * 3! * 7!
Calculating the total number of ways:
- 4! = 4 x 3 x 2 x 1 = 24
- 3! = 3 x 2 x 1 = 6
- 7! = 5040
- Total number of ways = 24 * 6 * 5040
- Total number of ways = 144 * 5040
- Total number of ways = 725760
Therefore, the correct answer is option C) 144.
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In how many ways can 4 boys and 3 girls be seated in a row of 7 chairs if the boys and girls alternate?a)120b)140c)144d)288Correct answer is option 'C'. Can you explain this answer?
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In how many ways can 4 boys and 3 girls be seated in a row of 7 chairs if the boys and girls alternate?a)120b)140c)144d)288Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In how many ways can 4 boys and 3 girls be seated in a row of 7 chairs if the boys and girls alternate?a)120b)140c)144d)288Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways can 4 boys and 3 girls be seated in a row of 7 chairs if the boys and girls alternate?a)120b)140c)144d)288Correct answer is option 'C'. Can you explain this answer?.
In how many ways can 4 boys and 3 girls be seated in a row of 7 chairs if the boys and girls alternate?a)120b)140c)144d)288Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In how many ways can 4 boys and 3 girls be seated in a row of 7 chairs if the boys and girls alternate?a)120b)140c)144d)288Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways can 4 boys and 3 girls be seated in a row of 7 chairs if the boys and girls alternate?a)120b)140c)144d)288Correct answer is option 'C'. Can you explain this answer?.
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