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JEE Main201911 Jan 2019Evening ShiftMathematicsProbabilityActual

Let S = 1,2, . ., 20 . A subset B of S is said to be "nice", if the sum of the elements of B is 203 . Than the probability that a randomly chosen subset of S is "nice" is :

Options

  1. A7 2²⁰
  2. B5 2²⁰
  3. C4 2²⁰
  4. DNone of the above

Correct answer

B. 5 2²⁰

Step-by-step solution

Since total number of subsets of the set S=2²⁰ Now, the sum of all number from 1 to 20= 20 21 2 =210 Then, find the sets which has sum 7 . (1) 7 (2) 1,6 (3) 2,5 (4) 3,4 (5) 1,2,4 Then, there is only 5 sets which has sum 203 Hence required probability = 5 2²⁰

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