Derangements (intro)
Permutations and combinations · Mathematics
Study notes
Q: 4 letters into 4 addressed envelopes, none correct. How many ways? Also: 3 letters? !4 = 4!(1 - 1 + 1/2 - 1/6 + 1/24) = 24 x 9/24 = 9. !3 = 3!(1 - 1 + 1/2 - 1/6) = 6 x 1/3 = 2. (The two cyclic swaps.)