Mathlean · Online math workspace
Derangement calculator
Count permutations in which no object remains in its original position.
How to use this calculator
Replace 5; five distinct objects have 44 derangements.
Tap the math below to edit it and see the result. Once a result is ready, press Tab on a hardware keyboard to accept it. Outside a matrix, Return completes the line; the phone math keyboard has the same Return action.
Try it here
Interactive tools require JavaScript. You can read the guide and example without it.
What to know
Objects are assumed distinct. This is not the number of all permutations.
Mathlean combines visual mathematical input with computation and canvas tools. Results depend on the expression and available engine support; check important answers independently.