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2014-10-24T02:04:49+05:30

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It is not clear if the question rightly posed..

A person can go to hospital on any of the 7 days.  So 7 ways of doing it.
Eight persons are independent.  So total number of ways in which all people can go to hospital on 7 days of a week are :   7^8.

Atmost 7 people can go to hospital on different days.  So the 8th person has to go to hospital on some day on which another person has already gone to hospital.

SO probability is equal to 1.

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