Question

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On a rainy day, five gentlemen A, B.C.D. E attend a party after leaving their umbrellas in a checkroom. After the party is over. the umbrellas get mixed up and are returned to the gentlemen in such a manner that none receives his own umbrella In how many ways can this happen?

Answer 1

Answer:

in 25ways it can happen

Answer 2

Answer:

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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