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