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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

Derangement D(n): number of permutations where no element is in original position. D(4) =

Answer: 9.

  • A 9
  • B 8
  • C 12
  • D 24

Correct answer: A. 9

Explanation: Inclusion-exclusion: D(4) = 4!(1−1+1/2!−1/3!+1/4!) = 24(1/2−1/6+1/24) = 24(12/24−4/24+1/24) = 24×9/24 = 9.

StartABCBCACAB6 ordered outcomes (permutations); pairing AB/BA etc gives 3 combinations

Counting tree for selecting 2 items from {A, B, C} without repetition: 3 x 2 = 6 ordered arrangements.

Concept context

Counting, arrangements, and selections

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