Question

6. On a rainy day n people go to a party in a hotel. Each of them leaves his umbrella at the proper
counter. Find the number of ways in which the umbrellas are handed back to them after the party
such a manner that no person receives his own umbrella.
are the one con​

Answer 1

Number of ways in which no person receives his own umbrella:-

= n![1−  (1/1!) + (1/2!) - (1/3!) +....(1/n!)].

Given in the question,  n people go to a party in a hotel.

Each of them leaves his umbrella at the proper  counter.

We have to find  the number of ways in which the umbrellas are handed back to them after the party.

In such a manner that no person receives his own umbrella.

This is a question of derangements which means no one should receive the proper object.

The formula for derangements is given as:-

Number of Derangements = n![1−  (1/1!) + (1/2!) - (1/3!) +....(1/n!)].

Which is the answer,where n! denotes the factorial of n.

Hence this is the required answer.

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Answer 2

Answer:

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