Well, it's a convolution e to the minus z times one, one, one minus z. you, you just do the convolution of the coefficient of the z to the n in that is the sum of k from zero to n and minus one to the k over k factorial. and that's a straight convolution and then that's a sum that we looked at as one of our examples for bounding the tail in the asymptotics lecture to show that's asintotic to one over e, that's very close to one over e. we're gonna look at an easier way to get this at the end of this lecture. but the symbolic method gets us there and then provides a practical solution to this kind of problem. the actual chance that if you go to a party and get yourself in a state of inebriation and wind up in a random room. you've got a pretty good probability that nobody ends up in their own room, 36%. or maybe a way to tell your parents about this problem is when students graduate and throw their hats in the air and everybody catches a random hat, 36% probability nobody gets their hats back. actually your parents probably want you to get your, or the rental company probably wants you to get your own hat back. and so there's the idea of generalized derangements so if, if you've got a random hat, you can always get your own hat back by following the cy cle. 