Question

A, B, C, D, E sit in a row. B is not at an end, and C is to the left of D. How many arrangements are possible?

• A. 24
  
• B. 36
  
• C. 48
  
• D. 60
  

Hint:

Apply restrictions sequentially, using fractions or direct placement for efficiency.

Answer 1

The Correct Option is B

- Step 1: Total arrangements. 5 people: $5! = 120$.
- Step 2: B not at ends. Ends = 1, 5. B in 2, 3, 4: $3/5$ positions. Total = $120 \times \frac{3}{5} = 72$.
- Step 3: C left of D. In any arrangement, C is left of D in half: $72 \div 2 = 36$.
- Step 4: Alternative. Place B in 2, 3, 4: 3 choices. Arrange C, D (C left of D) and A, E: $3 \times 2 \times 3! = 3 \times 2 \times 6 = 36$.
- Step 5: Compare with options. Options: (1) 24, (2) 36, (3) 48, (4) 60. Matches 36.
- Step 6: Conclusion. Option (2) is correct.