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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

Number of ways to select at least one from n objects:

Answer: 2 n - 1.

  • A 2<sup>n</sup>
  • B 2<sup>n</sup> - 1
  • C n!
  • D n

Correct answer: B. 2<sup>n</sup> - 1

Explanation: Total subsets = 2<sup>n.</sup> Excluding empty set: 2<sup>n</sup> - 1 ways to select at least one object.

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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