n objects are distributed at random among n p | vedclass

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(D) The total number of ways to distribute $n$ distinct objects among $n$ distinct persons is $n^n$. Each person can receive any number of objects. Th

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$n^n - n!$

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(D) The total number of ways to distribute $n$ distinct objects among $n$ distinct persons is $n^n$. Each person can receive any number of objects. The number of ways in which each person gets exactly one object is given by the number of permutations of $n$ objects taken $n$ at a time, which is $n!$. If each person gets exactly one object, then no person is left without an object. Therefore, the number of ways in which at least one person does not get any object is the total number of ways minus the number of ways where everyone gets exactly one object. Required number of ways $= n^n - n!$.

$n$ objects are distributed at random among $n$ persons. The number of ways in which this can be done so that at least one of them will not get any object is

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