Question

A, B, C, D sit around a circular table. A is opposite B. How many arrangements are possible?

• A. 2
  
• B. 4
  
• C. 6
  
• D. 8
  

Hint:

For opposite pairs in circular arrangements, fix one pair and arrange others.

Answer 1

The Correct Option is A

- Step 1: Total circular arrangements. 4 people: $(4-1)! = 3! = 6$.
- Step 2: A opposite B. Fix A at position 1, B at 3 (opposite). Arrange C, D in 2 remaining: $2! = 2$.
- Step 3: Verify. Only 2 ways: A-B opposite, C-D in remaining.
- Step 4: Compare with options. Options: (1) 2, (2) 4, (3) 6, (4) 8. Matches 2.
- Step 5: Conclusion. Option (1) is correct.