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If 10 objects are distributed at random ...

If 10 objects are distributed at random among 10 persons, then find the probability that at least one of them will not get anything.

Text Solution

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Each of the 10 objects can be given to any one of the 10 persons.
So, total number of ways = `10^(10)`
The number of ways of distribution in which each one gets exactly one object is `10!`.
So, the number of ways of distribution in which at least one of them does not get any object is `(10^(10) - 10!)`.
`therefore` Required probability = `(10^(10) - 10!)/(10^(10))`
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