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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

nCr = nC(n-r). So 10C3 = 10C?

Answer: 7.

  • A 7
  • B 3
  • C 6
  • D 4

Correct answer: A. 7

Explanation: 10C3 = 10C(10-3) = 10C7. So 10C3 = 10C7.

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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