In how many ways can 7 people be seated at a roundtable if 2 particular people must notsit next to each other?
- 5040
- 240
- 480
- 720
The Correct Option is C
Solution and Explanation
For circular arrangement of \(n\) people the formula = \((n - 1)!\)
Given that 7 people in the question so it will be \(6!\) = 720 (without any restrictions)
In question it is given that 2 particular people must not sit next to each other
making it \(5!\) for two people it will be \(5! \times 2 =240\)
In restricted cases from the total arrangements = 720 - 240 = 480
The correct option is (C): 480
Top Questions on Seating Arrangement
Four teams – Red (R), Blue (B), Green (G), and Yellow (Y) – are competing in the final four rounds of the Inter-School Science Olympiad, labeled Round A, Round B, Round C, and Round D. Each round consists of one match between two teams, and every team plays exactly two matches. No team plays the same opponent more than once.
The final schedule must adhere to the following rules:
- Rule 1 (Consecutive Play): The Green team (G) must play their two matches in consecutive rounds.
- Rule 2 (Fixed Appearance): The Yellow team (Y) must play in Round B.
- Rule 3 (Positional Constraint): The Red team (R) must play against the Blue team (B) in a round that is immediately before a round in which neither R nor B is playing.
- Rule 4 (Timing): The Blue team's (B) first match must occur in an earlier round than the Green team's (G) first match.
- Rule 5 (Opponent Link): The team that plays against the Red team (R) in the round that is not against the Blue team (B), is the same team that plays in Round D.
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