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A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers? 
  • a)
    7! – 2!3!2!
  • b)
    7! – 4!3!
  • c)
    7! – 5!3!
  • d)
    7 × 2!3!2!
  • e)
    2!3!2!  
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A group of four women and three men have tickets for seven adjacent se...
The first thing to recognize here is that this is a permutation with restrictions quest ion. In such questions it is always easiest to tackle the restricted scenario(s) first. The restricted case here is when all of the men actually sit together in three adjacent seats. Restrict ions can often be dealt with by considering the limited individuals as one unit. In this case we have four women ( w1, w2, w3, and w4) and three men (m1, m2, and m3). We can consider the men as one unit, since we can think of the 3 adjacent seats as simply 1 seat. If the men are one unit (m), we are really looking at seating 5 individuals ( w1, w2, w3, w4, and m) in 5 seats. There are 5! ways of arranging 5 individuals in a row. This means that our group of three men is sitting in any of the “five” seats. Now, imagine that the one seat that holds the three men magically splits into three seats. How many different ways can the men arrange themselves in those three seats? 3!. To calculate the total number of ways that the men and women can be arranged in 7 seats such that the men ARE sitting together, we must multiply these two values: 5!3!. However this problem asks for the number of ways the theatre-goers can be seated such that the men are NOT seated three in a row. Logically, this must be equivalent to the following: (Total number of all seat arrangements) – (Number of arrangements with 3 men in a row). The total number of all seat arrangements is simply 7! so the final calculat ion is 7! – 5!3!.
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A group of four women and three men have tickets for seven adjacent se...
The three men cannot sit together, so they must be seated in a way that ensures they are not adjacent. There are three possible ways to arrange the three men within the group of seven seats: the first man can sit in one of the four end seats, the second man can sit in one of the three remaining end seats, or the third man can sit in one of the two remaining end seats. Once the men are seated, the four women can be seated in any arrangement. So the total number of possible seating arrangements is 3 * 4! = 3 * 24 = 72. Answer: \boxed{72}.
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A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?a)7! – 2!3!2!b)7! – 4!3!c)7! – 5!3!d)7 × 2!3!2!e)2!3!2! Correct answer is option 'C'. Can you explain this answer?
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A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?a)7! – 2!3!2!b)7! – 4!3!c)7! – 5!3!d)7 × 2!3!2!e)2!3!2! Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?a)7! – 2!3!2!b)7! – 4!3!c)7! – 5!3!d)7 × 2!3!2!e)2!3!2! Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?a)7! – 2!3!2!b)7! – 4!3!c)7! – 5!3!d)7 × 2!3!2!e)2!3!2! Correct answer is option 'C'. Can you explain this answer?.
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