If n objects are distributed at random among n persons, the probability that at least one of them will not get anything is

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None of these

_{$1 - \frac{(n - 1)!}{n^{n}}$}

_{$\frac{(n - 1)!}{n^{n}}$}

_{$1 - \frac{(n - 1)!}{n^{n - 1}}$}

answer is A.

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Detailed Solution

The first object can be given to any of the n persons, but the second, third and other objects; too, can go to any of the n persons.

Therefore the total number of ways of distributing the n objects randomly among n persons is_$n^{n}$ .

There are _{$n_{P_{n}} = n!$} ways in which each person gets exactly one object,

so the probability of this happening is _{$\frac{n!}{n^{n}} = \frac{(n - 1)!}{n^{n - 1}}$} .

Hence the probability that at least one person does not get any object is =_{$1 - \frac{(n - 1)!}{n^{n - 1}}$}

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