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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

How many ways can 10 people be divided into two groups of 5?

Answer: 10C5 / 2 = 126.

  • A 10C5, the unsimplified combination count
  • B 10C5 / 2 = 126
  • C 10P5, treating order as significant
  • D 252, double the actual correct count

Correct answer: B. 10C5 / 2 = 126

Explanation: 10C5 = 252. But groups are unordered (not labeled), so divide by 2: 252/2 = 126.

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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