Question

A, B, C, D are four friends. A and B always sit together. How many ways can they sit in a row?

• A. 12
  
• B. 24
  
• C. 36
  
• D. 48
  

Hint:

For group seating, treat grouped individuals as a single unit and multiply by internal arrangements.

Answer 1

The Correct Option is A

- Step 1: Treat A and B as a unit. Units: (AB), C, D = 3 units.
- Step 2: Arrange units. $3! = 6$.
- Step 3: Arrange A and B within unit. AB or BA: $2! = 2$.
- Step 4: Calculate total. $6 \times 2 = 12$.
- Step 5: Verify. Total without restriction = $4! = 24$. A and B together in half (adjacent pairs): $\frac{24}{2} = 12$.
- Step 6: Compare with options. Options: (1) 12, (2) 24, (3) 36, (4) 48. Matches 12.
- Step 7: Conclusion. Option (1) is correct.