Derangement probabilities for the symmetric group of degree n acting on k sets: decreases are shown in bold
n\k	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35
2	0.50000
3	0.33333
4	0.37500	0.58333
5	0.36667	0.45000
6	0.36806	0.42222	0.63750
7	0.36786	0.44841	0.50952
8	0.36788	0.44911	0.49963	0.66230
9	0.36788	0.44576	0.48522	0.55181
10	0.36788	0.44601	0.50533	0.53230	0.68679
11	0.36788	0.44633	0.50476	0.52233	0.58029
12	0.36788	0.44628	0.50495	0.51473	0.56550	0.70123
13	0.36788	0.44625	0.50300	0.53009	0.55395	0.60280
14	0.36788	0.44626	0.50327	0.53204	0.55095	0.58355	0.71497
15	0.36788	0.44626	0.50333	0.53179	0.54534	0.57687	0.62073
16	0.36788	0.44626	0.50346	0.53151	0.55850	0.56946	0.60501	0.72448
17	0.36788	0.44626	0.50343	0.53024	0.55925	0.56699	0.59374	0.63570
18	0.36788	0.44626	0.50342	0.53021	0.55999	0.56309	0.59101	0.61801	0.73432
19	0.36788	0.44626	0.50341	0.53034	0.55944	0.57406	0.58482	0.60903	0.64801
20	0.36788	0.44626	0.50342	0.53040	0.55927	0.57575	0.58414	0.60347	0.63266	0.74119
21	0.36788	0.44626	0.50342	0.53047	0.55833	0.57584	0.58071	0.59974	0.62154	0.65898
22	0.36788	0.44626	0.50342	0.53046	0.55840	0.57609	0.59062	0.59609	0.61809	0.64221	0.74847
23	0.36788	0.44626	0.50342	0.53045	0.55841	0.57571	0.59175	0.59528	0.61292	0.63269	0.66823
24	0.36788	0.44626	0.50342	0.53044	0.55850	0.57550	0.59251	0.59274	0.61131	0.62738	0.65323	0.75382
25	0.36788	0.44626	0.50342	0.53044	0.55853	0.57481	0.59234	0.60138	0.60810	0.62420	0.64253	0.67658
26	0.36788	0.44626	0.50342	0.53044	0.55857	0.57477	0.59253	0.60288	0.60801	0.62030	0.63829	0.66065	0.75948
27	0.36788	0.44626	0.50342	0.53044	0.55855	0.57483	0.59212	0.60337	0.60566	0.61883	0.63364	0.65139	0.68398
28	0.36788	0.44626	0.50342	0.53044	0.55855	0.57486	0.59198	0.60367	0.61356	0.61654	0.63197	0.64542	0.66939	0.76383
29	0.36788	0.44626	0.50342	0.53044	0.55854	0.57491	0.59139	0.60354	0.61470	0.61635	0.62851	0.64220	0.65908	0.69069
30	0.36788	0.44626	0.50342	0.53044	0.55854	0.57493	0.59139	0.60356	0.61548	0.61452	0.62790	0.63948	0.65456	0.67548	0.76847
31	0.36788	0.44626	0.50342	0.53044	0.55854	0.57496	0.59139	0.60325	0.61552	0.62155	0.62578	0.63721	0.64978	0.66630	0.69670
32	0.36788	0.44626	0.50342	0.53044	0.55854	0.57495	0.59144	0.60309	0.61574	0.62298	0.62591	0.63478	0.64798	0.66064	0.68259	0.77205
33	0.36788	0.44626	0.50342	0.53044	0.55854	0.57495	0.59146	0.60263	0.61553	0.62350	0.62416	0.63408	0.64518	0.65682	0.67275	0.70230
34	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59150	0.60259	0.61555	0.62382	0.63083	0.63251	0.64387	0.65401	0.66798	0.68769	0.77596
35	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60261	0.61525	0.62386	0.63187	0.63255	0.64163	0.65219	0.66310	0.67861	0.70733
36	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59154	0.60263	0.61515	0.62394	0.63264	0.63110	0.64139	0.64991	0.66121	0.67312	0.69366	0.77904
37	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59153	0.60267	0.61475	0.62377	0.63277	0.63714	0.63984	0.64863	0.65844	0.66909	0.68406	0.71206
38	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59153	0.60268	0.61473	0.62374	0.63301	0.63841	0.64012	0.64691	0.65733	0.66617	0.67933	0.69799	0.78235
39	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60271	0.61472	0.62351	0.63294	0.63895	0.63870	0.64663	0.65509	0.66430	0.67450	0.68911	0.71639
40	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61475	0.62339	0.63302	0.63932	0.64442	0.64547	0.65440	0.66238	0.67233	0.68375	0.70309	0.78502
41	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60274	0.61476	0.62306	0.63282	0.63940	0.64546	0.64561	0.65278	0.66088	0.66959	0.67962	0.69373	0.72046
42	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60273	0.61480	0.62302	0.63281	0.63950	0.64619	0.64442	0.65274	0.65928	0.66845	0.67659	0.68907	0.70688	0.78791
43	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60273	0.61481	0.62303	0.63259	0.63946	0.64637	0.64971	0.65157	0.65850	0.66646	0.67461	0.68431	0.69814	0.72422
44	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60273	0.61483	0.62304	0.63250	0.63948	0.64664	0.65085	0.65188	0.65726	0.66550	0.67277	0.68190	0.69289	0.71129	0.79024
45	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62306	0.63220	0.63932	0.64662	0.65141	0.65071	0.65715	0.66396	0.67155	0.67921	0.68878	0.70220	0.72780
46	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61485	0.62307	0.63218	0.63928	0.64673	0.65180	0.65575	0.65622	0.66355	0.66984	0.67797	0.68574	0.69752	0.71461	0.79280
47	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61485	0.62310	0.63217	0.63910	0.64664	0.65192	0.65671	0.65645	0.66230	0.66889	0.67606	0.68356	0.69288	0.70603	0.73110
48	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62311	0.63219	0.63901	0.64665	0.65205	0.65739	0.65544	0.66238	0.66771	0.67526	0.68169	0.69042	0.70093	0.71851	0.79487
49	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62312	0.63219	0.63875	0.64650	0.65205	0.65764	0.66013	0.66146	0.66723	0.67358	0.68044	0.68757	0.69680	0.70965	0.73427
50	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63222	0.63871	0.64647	0.65209	0.65792	0.66119	0.66178	0.66625	0.67300	0.67907	0.68629	0.69380	0.70500	0.72145	0.79714
51	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62314	0.63223	0.63872	0.64629	0.65202	0.65793	0.66175	0.66078	0.66625	0.67182	0.67798	0.68444	0.69150	0.70046	0.71307	0.73722
52	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62314	0.63225	0.63872	0.64622	0.65201	0.65805	0.66211	0.66529	0.66551	0.67156	0.67670	0.68359	0.68961	0.69795	0.70801	0.72492	0.79901
53	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61483	0.62313	0.63225	0.63873	0.64599	0.65187	0.65801	0.66229	0.66619	0.66576	0.67059	0.67605	0.68215	0.68824	0.69512	0.70394	0.71626	0.74005
54	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61483	0.62313	0.63227	0.63874	0.64596	0.65183	0.65805	0.66244	0.66685	0.66489	0.67073	0.67515	0.68143	0.68692	0.69368	0.70100	0.71167	0.72758	0.80105
55	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61483	0.62313	0.63227	0.63876	0.64595	0.65169	0.65796	0.66246	0.66711	0.66911	0.66995	0.67485	0.68016	0.68602	0.69185	0.69861	0.70722	0.71934	0.74270
56	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63228	0.63877	0.64596	0.65161	0.65795	0.66253	0.66738	0.67009	0.67030	0.67405	0.67977	0.68475	0.69094	0.69661	0.70467	0.71439	0.73068	0.80273
57	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63228	0.63879	0.64596	0.65141	0.65782	0.66249	0.66744	0.67063	0.66942	0.67412	0.67884	0.68399	0.68956	0.69526	0.70189	0.71034	0.72224	0.74526
58	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63228	0.63880	0.64598	0.65137	0.65779	0.66250	0.66758	0.67099	0.67350	0.67350	0.67870	0.68298	0.68894	0.69391	0.70033	0.70744	0.71766	0.73309	0.80459
59	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63227	0.63881	0.64599	0.65137	0.65764	0.66242	0.66755	0.67118	0.67436	0.67377	0.67790	0.68255	0.68764	0.69297	0.69845	0.70503	0.71329	0.72500	0.74767
60	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63227	0.63881	0.64600	0.65137	0.65758	0.66240	0.66761	0.67134	0.67498	0.67300	0.67807	0.68182	0.68715	0.69194	0.69754	0.70305	0.71077	0.72014	0.73591	0.80613
61	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63227	0.63882	0.64601	0.65138	0.65739	0.66228	0.66755	0.67139	0.67524	0.67685	0.67742	0.68162	0.68615	0.69109	0.69616	0.70156	0.70798	0.71612	0.72763	0.74999
62	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63227	0.63881	0.64603	0.65139	0.65737	0.66224	0.66756	0.67146	0.67552	0.67776	0.67776	0.68096	0.68588	0.69008	0.69551	0.70020	0.70638	0.71326	0.72311	0.73810	0.80781
63	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63227	0.63881	0.64603	0.65140	0.65735	0.66212	0.66748	0.67145	0.67560	0.67828	0.67698	0.68107	0.68513	0.68953	0.69439	0.69923	0.70445	0.71085	0.71881	0.73016	0.75219
64	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63227	0.63881	0.64604	0.65141	0.65736	0.66206	0.66746	0.67148	0.67573	0.67864	0.68072	0.68054	0.68507	0.68873	0.69379	0.69822	0.70348	0.70886	0.71629	0.72538	0.74066	0.80923
65	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63227	0.63881	0.64604	0.65142	0.65736	0.66189	0.66735	0.67143	0.67574	0.67883	0.68152	0.68082	0.68439	0.68842	0.69278	0.69749	0.70212	0.70729	0.71354	0.72138	0.73255	0.75431
66	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63227	0.63881	0.64605	0.65143	0.65738	0.66186	0.66732	0.67142	0.67582	0.67900	0.68211	0.68013	0.68458	0.68782	0.69243	0.69649	0.70147	0.70592	0.71190	0.71858	0.72809	0.74268	0.81078
67	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63227	0.63881	0.64605	0.65144	0.65738	0.66185	0.66720	0.67135	0.67577	0.67907	0.68238	0.68366	0.68403	0.68770	0.69161	0.69586	0.70036	0.70492	0.70998	0.71614	0.72384	0.73487	0.75632
68	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63227	0.63881	0.64605	0.65144	0.65739	0.66185	0.66715	0.67132	0.67581	0.67915	0.68266	0.68453	0.68436	0.68714	0.69143	0.69504	0.69985	0.70387	0.70891	0.71418	0.72132	0.73017	0.74503	0.81208
69	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63227	0.63881	0.64604	0.65145	0.65740	0.66186	0.66699	0.67123	0.67574	0.67916	0.68275	0.68503	0.68366	0.68727	0.69081	0.69465	0.69882	0.70315	0.70756	0.71257	0.71862	0.72621	0.73707	0.75828
70	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63227	0.63881	0.64604	0.65145	0.65741	0.66186	0.66697	0.67119	0.67574	0.67920	0.68290	0.68537	0.68711	0.68682	0.69079	0.69398	0.69839	0.70231	0.70687	0.71114	0.71696	0.72343	0.73266	0.74688	0.81351
Limits	0.36788	0.44626	0.50342	0.53044	0.55854	0.57494	0.59152	0.60272	0.61484	0.62313	0.63227	0.63881	0.64604	0.65145	0.65744	0.66193	0.66703	0.67092	0.67527	0.67868	0.6825	0.6855	0.6889	0.69158	0.69461	0.69705	0.69978	0.70199	0.70449