File:Permutationen und Derangements.png
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| Description |
English: Number of n-permutations and complete derangements of n elements, i.e. permutations where none of its elements remains at its initial place
Deutsch: Zahl der Permutationen und (totalen) Derangements von n Elementen. d.h. Permutationen, bei denen keines der Elemente an seinem ursprünglichen Platz verbleibt |
| Date | |
| Source | Own work |
| Author | Qniemiec |
| n | Derangement , D (n ) | Permutation , P (n ) | ||
|---|---|---|---|---|
| 0 | 1 | (1×100) | 1 | (1×100) |
| 1 | 0 | (0) | 1 | (1×100) |
| 2 | 1 | (1×100) | 2 | (2×100) |
| 3 | 2 | (2×100) | 6 | (6×100) |
| 4 | 9 | (9×100) | 24 | (2.4×101) |
| 5 | 44 | (4.4×101) | 120 | (1.20×102) |
| 6 | 265 | (2.65×102) | 720 | (7.20×102) |
| 7 | 1 854 | (1.85×103) | 5 040 | (5.04×103) |
| 8 | 14 833 | (1.48×104) | 40 320 | (4.03×104) |
| 9 | 133 496 | (1.33×105) | 362 880 | (3.63×105) |
| 10 | 1 334 961 | (1.33×106) | 3 628 800 | (3.63×106) |
| 11 | 14 684 570 | (1.47×107) | 39 916 800 | (3.99×107) |
| 12 | 176 214 841 | (1.76×108) | 479 001 600 | (4.79×108) |
| 13 | 2 290 792 932 | (2.29×109) | 6 227 020 800 | (6.23×109) |
| 14 | 32 071 101 049 | (3.21×1010) | 87 178 291 200 | (8.72×1010) |
| 15 | 481 066 515 734 | (4.81×1011) | 1 307 674 368 000 | (1.31×1012) |
| 16 | 7 697 064 251 745 | (7.70×1012) | 20 922 789 888 000 | (2.09×1013) |
| 17 | 130 850 092 279 664 | (1.31×1014) | 355 687 428 096 000 | (3.56×1014) |
| 18 | 2 355 301 661 033 953 | (2.36×1015) | 6 402 373 705 728 000 | (6.40×1015) |
| 19 | 44 750 731 559 645 106 | (4.48×1016) | 121 645 100 408 832 000 | (1.22×1017) |
| 20 | 895 014 631 192 902 121 | (8.95×1017) | 2 432 902 008 176 640 000 | (2.43×1018) |
See also: File:Kombinationen und Variationen.png.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 15:35, 15 May 2011 | | 640 × 400 (3 KB) | Qniemiec (talk | contribs) | {{Information |Description ={{en|1=Number of n-permutations and complete derangements of n elements, i.e. permutations where none of its elements remains at its initial place}} {{de|1=Zahl der Permutationen und (totalen) Derangements von n Elementen. d |
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