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When n objects are assigned randomly to n people, what is the probability that at least one person receives no object?
- 1 - (n-1)!/(n^(n-1))
- (n-1)!/(nⁿ)
- 1 - (n-1)!/(nⁿ)
- None of these
Correct answer: 1 - (n-1)!/(n^(n-1))
Solution
The correct option represents the probability that at least one person does not receive an object, which is derived from the total arrangements of objects and the arrangements where each person receives at least one object. By calculating the complement of the scenario where everyone receives at least one object, we arrive at the expression 1 - (n-1)!/(n^(n-1)).
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