Counting umbrellas

Five gentlemen attend a party. Since it was raining , all of them carried an umbrella each . However , when the party was over , the umbrellas were jumbled and lay in 1 big pile. In how many ways can the umbrellas be given back to them such that the number of men receiving their own umbrella is lesser than the number of men receiving someone else’s umbrella.

Bonus - Generalise to ‘n’ gentlemen


The answer is 109.

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