CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations
Seven distinct people, including Meera and Nikhil, are to be seated in a row. In how many ways can they be seated so that Meera and Nikhil are NOT seated next to each other?
The answer is 3600. All seven people can be seated in 7! = 5040 ways. When Meera and Nikhil sit together, treating them as one block gives 6! × 2 = 1440 ways. Subtracting gives 5040 − 1440 = 3600 arrangements.
- A720
- B1440
- C3600Correct
- D3840
Explanation
Total arrangements = 7! = 5040. Arrangements with Meera and Nikhil together = 6! × 2 = 1440. Not together = 5040 − 1440 = 3600. The value 1440 is the 'together' count, and 720 is 6! alone.
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