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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

In a group of 10 people, handshakes if everyone shakes everyone else exactly once:

Answer: 45.

  • A 10
  • B 45
  • C 90
  • D 100

Correct answer: B. 45

Explanation: Each handshake = 1 unique pair of people. Count pairs from 10: C(10,2) = 10×9/2 = 45. Order within a pair doesn't matter, so no doubling.

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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