A probability problem by A Former Brilliant Member

Probability Level 3

Six friends are going to give each other gifts in a such a way that everybody gives one gift and receives one . In how many ways is this possible?

Condition: No one should receive his own gift.


The answer is 265.

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A Former Brilliant Member by A Former Brilliant Member

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1 solution

Relevant wiki: Derangements

Using the derangement formula = 6 ! ( 1 1 − 1 1 + 1 2 − 1 6 + 1 24 − 1 120 + 1 720 ) = 720 ( 53 144 ) = 265 6!(\frac{1}{1} - \frac{1}{1} +\frac{1}{2} - \frac{1}{6} + \frac{1}{24} -\frac{1}{120} + \frac{1}{720}) = 720(\frac{53}{144}) = 265

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