The letters A, B, C, D and E are arranged in such a way that there are exactly two letters between A and E. How many such arrangements are possible?
Answer & explanation
Answer: (c) 24
In a row of five, A and E can stand only at places 1 and 4 or 2 and 5, in either order: 4 ways. The other three letters then fill the remaining places in 3! = 6 ways, giving 24.
- Number the places 1 to 5. Exactly two letters between A and E means A and E occupy places (1, 4) or (2, 5): 2 choices of places.
- A and E can swap within the chosen places: 2 × 2 = 4 ways.
- B, C and D fill the other three places in 3! = 6 ways.
- Total = 4 × 6 = 24.
Remember · Place the constrained pair first (positions × internal order), then arrange the remaining items freely.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·