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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

The number of permutations of n things taken all at once when p are alike:

Answer: n!/p!.

  • A n!/p!
  • B n! × p!
  • C p!/n!
  • D (n-p)!

Correct answer: A. n!/p!

Explanation: When p items are identical: permutations = n!/p!. Divides by repetitions.

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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