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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. Then the probability that a randomly chosen subset of S is "nice" is:
- 5/2²⁰
- 7/2²⁰
- 4/2²⁰
- 6/2²⁰
Correct answer: 5/2²⁰
Solution
The total sum of the elements in set S is 210, and for a subset B to have a sum of 203, it must exclude elements that sum to 7. There are 5 subsets of S that can achieve this by excluding combinations of elements that total 7, leading to a probability of 5 out of the total 2²⁰ possible subsets.
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