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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

The number of diagonals of a convex 12-sided polygon is:

Answer: 54.

  • A 48
  • B 54
  • C 60
  • D 66

Correct answer: B. 54

Explanation: Diagonals = n(n−3)/2 = 12·9/2 = 54.

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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