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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

Number of binary strings of length n with exactly k ones:

Answer: C(n,k).

  • A n<sup>k</sup>
  • B C(n,k)
  • C k!/(n-k)!
  • D 2<sup>n</sup>

Correct answer: B. C(n,k)

Explanation: A binary string of length n with exactly k ones: choose k positions (out of n) to place the 1s; the rest become 0s. Number of ways = C(n,k).

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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