Another update from ingydotnet^djgoku

Task/Permutations-Derangements/00DESCRIPTION

@@ -18,3 +18,4 @@ As an optional stretch goal:
 ;Cf.
 * [[Anagrams/Deranged anagrams]]
 * [[Best shuffle]]
+* [[Left_factorials]]

Task/Permutations-Derangements/Elixir/permutations-derangements.elixir

@@ -0,0 +1,29 @@
+defmodule Permutation do
+  def derangements(n) do
+    list = Enum.to_list(1..n)
+    Enum.filter(permutation(list), fn perm ->
+      Enum.zip(list, perm) |> Enum.all?(fn {a,b} -> a != b end)
+    end)
+  end
+
+  def subfact(0), do: 1
+  def subfact(1), do: 0
+  def subfact(n), do: (n-1) * (subfact(n-1) + subfact(n-2))
+
+  def permutation([]), do: [[]]
+  def permutation(list) do
+    for x <- list, y <- permutation(list -- [x]), do: [x|y]
+  end
+end
+
+IO.puts "derangements for n = 4"
+Enum.each(Permutation.derangements(4), &IO.inspect &1)
+
+IO.puts "\nNumber of derangements"
+IO.puts " n    derange   subfact"
+Enum.each(0..9, fn n ->
+  :io.format "~2w :~9w,~9w~n", [n, length(Permutation.derangements(n)), Permutation.subfact(n)]
+end)
+Enum.each(10..20, fn n ->
+  :io.format "~2w :~19w~n", [n, Permutation.subfact(n)]
+end)