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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

Inclusion-Exclusion: |A ∪ B ∪ C| =

Answer: |A|+|B|+|C|-|A∩B|-|A∩C|-|B∩C|+|A∩B∩C|.

  • A |A|+|B|+|C|, leaving out all the overlaps between the sets
  • B |A|+|B|+|C|-|A∩B|-|A∩C|-|B∩C|+|A∩B∩C|
  • C |A|+|B|+|C|-|A∩B∩C|, subtracting just the triple overlap once
  • D |A∩B∩C|, taken as if it represented the entire union

Correct answer: B. |A|+|B|+|C|-|A∩B|-|A∩C|-|B∩C|+|A∩B∩C|

Explanation: Add singles, subtract pairwise intersections (over-subtracted), add back triple (under-subtracted). |A∪B∪C| = |A|+|B|+|C| − |A∩B| − |A∩C| − |B∩C| + |A∩B∩C|.

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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