Civil Services Prep

Prelims 2022 · CSAT / Quantitative Aptitude · Question 24

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?

  1. 12
  2. 18
  3. 24
  4. 36

Answer

24

  • Key fact: A and E must be placed with exactly two letters between them, so their positions can be (1,4), (2,5), (4,1), (5,2). That gives 4 ordered placements for A and E.
  • Remaining letters: After fixing A and E, the letters B, C and D can be arranged in the remaining 3 places in 3! = 6 ways.
  • Total arrangements: 4 × 6 = 24.
  • Option check:
    • (a) 12 Incorrect — undercounts the valid placements.
    • (b) 18 Incorrect — not obtained from the valid counting.
    • (c) 24 Correct — matches the total number of arrangements.
    • (d) 36 Incorrect — overcounts the arrangements.
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