Question

A large company with n employees has a scheme according to which each employee buys a...

A large company with n employees has a scheme according to which each employee buys a Christmas gift and the gifts are then distributed at random to the employees. What is the probability that someone gets his or her own gift?

Math   Statistics-And-Probability   
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Answer #1

The number of ways in which n gifts could be distributed among n employees such that no one gets his / her own gift is computed using the Derangement formula D(n) given as:

Also total number of ways in which n gifts could be given to n employees is given as the permutation of n items at n places = n!

Therefore the required probability that someone gets his or her own gift is computed as:

= 1 - Probability that no one gets his or her own gift

This is the required probability here.

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