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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

Catalan number Cₙ = C(2n,n)/(n+1). C₃ =

Answer: 5.

  • A 5
  • B 14
  • C 4
  • D 6

Correct answer: A. 5

Explanation: C₃ = C(6,3)/(3+1) = 20/4 = 5. Verify: C(6,3) = 6!/(3!3!) = 720/36 = 20. Catalan numbers count valid bracket sequences, triangulations, etc.

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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