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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

How many ways to arrange letters AABBCC?

Answer: 90.

  • A 90
  • B 720
  • C 180
  • D 360

Correct answer: A. 90

Explanation: 6 letters with A repeated 2×, B repeated 2×, C repeated 2×. Multinomial: 6!/(2!×2!×2!) = 720/8 = 90. Each of 90 arrangements is distinct.

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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