6-different-letters-were-written-to-6-different-people-and-6-different-envelopes-were-prepared-with-the-addresses-of-these-people-written-on-them-In-how-many-different-ways-can-you-put-a-letter-in-

Question Number 209263 by hardmath last updated on 05/Jul/24

$$ \\ $$6 different letters were written to 6 different people and 6 different envelopes were prepared with the addresses of these people written on them. In how many different ways can you put a letter in each envelope without putting a letter written to this person in the envelope with the name of any person?

Commented by mr W last updated on 05/Jul/24

$${number}\:{of}\:{derangement}\: \\ $$$$!\mathrm{6}=\mathrm{265}\:{ways} \\ $$

Commented by hardmath last updated on 05/Jul/24

$$\mathrm{Dear}\:\mathrm{professor}, \\ $$$$ \\ $$How does !6 = 265, that is 6! = 720, how is !6 calculated?

Commented by mr W last updated on 05/Jul/24

Commented by mr W last updated on 05/Jul/24

https://en.m.wikipedia.org/wiki/Derangement

Commented by hardmath last updated on 06/Jul/24

$$\mathrm{cool}\:\mathrm{dear}\:\mathrm{professor}\:\mathrm{thank}\:\mathrm{you} \\ $$

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