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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

The Stirling number S(n,k) counts:

Answer: Partitions of n-element set into k non-empty subsets.

  • A Arrangements of n objects that have exactly k fixed points
  • B Partitions of n-element set into k non-empty subsets
  • C The number of k-element combinations chosen from n objects
  • D n choose k, the ordinary binomial coefficient

Correct answer: B. Partitions of n-element set into k non-empty subsets

Explanation: Stirling numbers of the 2nd kind S(n,k): partition a set of n distinct elements into exactly k non-empty, unordered subsets. E.g. S(3,2)=3: {1},{2,3} and permutations.

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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