Conditional Probability

The initial step involves distributing the n objects among n persons.

Each object can be given to any of the n persons independently, so the total number of ways to distribute the objects is:

Total ways =

We now consider the case where each person gets exactly one object. This is a perfect one-to-one assignment or permutation, which can happen in:

Favorable ways =

So, the probability that each person gets exactly one object is:

But we are interested in the probability that at least one person does not get any object, which is the complement of the above case:

Required probability =

So, the final answer is:

The correct option is (D)