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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

nC(r-1) + nCr = ?

Answer: (n+1)Cr.

  • A nC(r+1)
  • B (n+1)Cr
  • C (n+1)C(r-1)
  • D (n-1)Cr

Correct answer: B. (n+1)Cr

Explanation: Pascal identity: nC(r-1) + nCr = (n+1)Cr. Basis of Pascal triangle.

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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