five different objects are distributed among 3 persons at random .what is the probability of that each person receive at least one object?
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Correct option is
A
1−
n
n−1
(n−1)!
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 objects, so the probability of this happening is
n
n
n!
=
n
n−1
(n−1)!
Hence the probability that at least one person does not get any objects is
1−
n
n−1
(n−1)!
Step-by-step explanation:
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