Reference 7Z78 Main

# Factorials and Combinations

by Richard Pavlicek

This page contains lookup charts for factorials from 0-52, and combinations (NcR) from 1-52.

 Reference 7Z78 Main Top Factorials and Combinations

## Factorials

The factorial of a number (N!) is the product of all integers from 1 through that number. The following table shows the value of all factorials from 0* to 52. The numbers increase rapidly up to 68 digits, so stand back and enjoy the Christmas tree.

*Zero factorial is defined as 1, not for some hidden mathematical beauty but because doing so works well in formulas.

NN Factorial (N!)
01
11
22
36
424
5120
6720
75040
840,320
9362,880
103,628,800
1139,916,800
12479,001,600
136,227,020,800
1487,178,291,200
151,307,674,368,000
1620,922,789,888,000
17355,687,428,096,000
186,402,373,705,728,000
19121,645,100,408,832,000
202,432,902,008,176,640,000
2151,090,942,171,709,440,000
221,124,000,727,777,607,680,000
2325,852,016,738,884,976,640,000
24620,448,401,733,239,439,360,000
2515,511,210,043,330,985,984,000,000
26403,291,461,126,605,635,584,000,000
2710,888,869,450,418,352,160,768,000,000
28304,888,344,611,713,860,501,504,000,000
298,841,761,993,739,701,954,543,616,000,000
30265,252,859,812,191,058,636,308,480,000,000
318,222,838,654,177,922,817,725,562,880,000,000
32263,130,836,933,693,530,167,218,012,160,000,000
338,683,317,618,811,886,495,518,194,401,280,000,000
34295,232,799,039,604,140,847,618,609,643,520,000,000
3510,333,147,966,386,144,929,666,651,337,523,200,000,000
36371,993,326,789,901,217,467,999,448,150,835,200,000,000
3713,763,753,091,226,345,046,315,979,581,580,902,400,000,000
38523,022,617,466,601,111,760,007,224,100,074,291,200,000,000
3920,397,882,081,197,443,358,640,281,739,902,897,356,800,000,000
40815,915,283,247,897,734,345,611,269,596,115,894,272,000,000,000
4133,452,526,613,163,807,108,170,062,053,440,751,665,152,000,000,000
421,405,006,117,752,879,898,543,142,606,244,511,569,936,384,000,000,000
4360,415,263,063,373,835,637,355,132,068,513,997,507,264,512,000,000,000
442,658,271,574,788,448,768,043,625,811,014,615,890,319,638,528,000,000,000
45119,622,220,865,480,194,561,963,161,495,657,715,064,383,733,760,000,000,000
465,502,622,159,812,088,949,850,305,428,800,254,892,961,651,752,960,000,000,000
47258,623,241,511,168,180,642,964,355,153,611,979,969,197,632,389,120,000,000,000
4812,413,915,592,536,072,670,862,289,047,373,375,038,521,486,354,677,760,000,000,000
49608,281,864,034,267,560,872,252,163,321,295,376,887,552,831,379,210,240,000,000,000
5030,414,093,201,713,378,043,612,608,166,064,768,844,377,641,568,960,512,000,000,000,000
511,551,118,753,287,382,280,224,243,016,469,303,211,063,259,720,016,986,112,000,000,000,000
5280,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000

 Reference 7Z78 Main Top Factorials and Combinations

## Combinations

The following tables show the number of combinations (NcR) for all values of N and R through 52. Find N at the top of a column, then the various values for R will be listed in order below.

RN=1N=2N=3N=4
01111
11234
2136
314
41

RN=5N=6N=7N=8
01111
15678
210152128
310203556
45153570
5162156
61728
718
81

RN=9N=10N=11N=12
01111
19101112
236455566
384120165220
4126210330495
5126252462792
684210462924
736120330792
8945165495
911055220
1011166
11112
121

RN=13N=14N=15N=16
01111
113141516
27891105120
3286364455560
4715100113651820
51287200230034368
61716300350058008
717163432643511,440
812873003643512,870
97152002500511,440
10286100130038008
117836413654368
1213914551820
13114105560
14115120
15116
161

RN=17N=18N=19N=20
01111
117181920
2136153171190
36808169691140
42380306038764845
56188856811,62815,504
612,37618,56427,13238,760
719,44831,82450,38877,520
824,31043,75875,582125,970
924,31048,62092,378167,960
1019,44843,75892,378184,756
1112,37631,82475,582167,960
12618818,56450,388125,970
132380856827,13277,520
14680306011,62838,760
15136816387615,504
16171539694845
171181711140
18119190
19120
201

RN=21N=22N=23N=24
01111
121222324
2210231253276
31330154017712024
459857315885510,626
520,34926,33433,64942,504
654,26474,613100,947134,596
7116,280170,544245,157346,104
8203,490319,770490,314735,471
9293,930497,420817,1901,307,504
10352,716646,6461,144,0661,961,256
11352,716705,4321,352,0782,496,144
12293,930646,6461,352,0782,704,156
13203,490497,4201,144,0662,496,144
14116,280319,770817,1901,961,256
1554,264170,544490,3141,307,504
1620,34974,613245,157735,471
17598526,334100,947346,104
181330731533,649134,596
192101540885542,504
2021231177110,626
211222532024
22123276
23124
241

RN=25N=26N=27N=28
01111
125262728
2300325351378
32300260029253276
412,65014,95017,55020,475
553,13065,78080,73098,280
6177,100230,230296,010376,740
7480,700657,800888,0301,184,040
81,081,5751,562,2752,220,0753,108,105
92,042,9753,124,5504,686,8256,906,900
103,268,7605,311,7358,436,28513,123,110
114,457,4007,726,16013,037,89521,474,180
125,200,3009,657,70017,383,86030,421,755
135,200,30010,400,60020,058,30037,442,160
144,457,4009,657,70020,058,30040,116,600
153,268,7607,726,16017,383,86037,442,160
162,042,9755,311,73513,037,89530,421,755
171,081,5753,124,5508,436,28521,474,180
18480,7001,562,2754,686,82513,123,110
19177,100657,8002,220,0756,906,900
2053,130230,230888,0303,108,105
2112,65065,780296,0101,184,040
22230014,95080,730376,740
23300260017,55098,280
2425325292520,475
251263513276
26127378
27128
281

RN=29N=30N=31N=32
01111
129303132
2406435465496
33654406044954960
423,75127,40531,46535,960
5118,755142,506169,911201,376
6475,020593,775736,281906,192
71,560,7802,035,8002,629,5753,365,856
84,292,1455,852,9257,888,72510,518,300
910,015,00514,307,15020,160,07528,048,800
1020,030,01030,045,01544,352,16564,512,240
1134,597,29054,627,30084,672,315129,024,480
1251,895,93586,493,225141,120,525225,792,840
1367,863,915119,759,850206,253,075347,373,600
1477,558,760145,422,675265,182,525471,435,600
1577,558,760155,117,520300,540,195565,722,720
1667,863,915145,422,675300,540,195601,080,390
1751,895,935119,759,850265,182,525565,722,720
1834,597,29086,493,225206,253,075471,435,600
1920,030,01054,627,300141,120,525347,373,600
2010,015,00530,045,01584,672,315225,792,840
214,292,14514,307,15044,352,165129,024,480
221,560,7805,852,92520,160,07564,512,240
23475,0202,035,8007,888,72528,048,800
24118,755593,7752,629,57510,518,300
2523,751142,506736,2813,365,856
26365427,405169,911906,192
27406406031,465201,376
2829435449535,960
291304654960
30131496
31132
321

RN=33N=34N=35N=36
01111
133343536
2528561595630
35456598465457140
440,92046,37652,36058,905
5237,336278,256324,632376,992
61,107,5681,344,9041,623,1601,947,792
74,272,0485,379,6166,724,5208,347,680
813,884,15618,156,20423,535,82030,260,340
938,567,10052,451,25670,607,46094,143,280
1092,561,040131,128,140183,579,396254,186,856
11193,536,720286,097,760417,225,900600,805,296
12354,817,320548,354,040834,451,8001,251,677,700
13573,166,440927,983,7601,476,337,8002,310,789,600
14818,809,2001,391,975,6402,319,959,4003,796,297,200
151,037,158,3201,855,967,5203,247,943,1605,567,902,560
161,166,803,1102,203,961,4304,059,928,9507,307,872,110
171,166,803,1102,333,606,2204,537,567,6508,597,496,600
181,037,158,3202,203,961,4304,537,567,6509,075,135,300
19818,809,2001,855,967,5204,059,928,9508,597,496,600
20573,166,4401,391,975,6403,247,943,1607,307,872,110
21354,817,320927,983,7602,319,959,4005,567,902,560
22193,536,720548,354,0401,476,337,8003,796,297,200
2392,561,040286,097,760834,451,8002,310,789,600
2438,567,100131,128,140417,225,9001,251,677,700
2513,884,15652,451,256183,579,396600,805,296
264,272,04818,156,20470,607,460254,186,856
271,107,5685,379,61623,535,82094,143,280
28237,3361,344,9046,724,52030,260,340
2940,920278,2561,623,1608,347,680
30545646,376324,6321,947,792
31528598452,360376,992
3233561654558,905
331345957140
34135630
35136
361

RN=37N=38N=39N=40
01111
137383940
2666703741780
37770843691399880
466,04573,81582,25191,390
5435,897501,942575,757658,008
62,324,7842,760,6813,262,6233,838,380
710,295,47212,620,25615,380,93718,643,560
838,608,02048,903,49261,523,74876,904,685
9124,403,620163,011,640211,915,132273,438,880
10348,330,136472,733,756635,745,396847,660,528
11854,992,1521,203,322,2881,676,056,0442,311,801,440
121,852,482,9962,707,475,1483,910,797,4365,586,853,480
133,562,467,3005,414,950,2968,122,425,44412,033,222,880
146,107,086,8009,669,554,10015,084,504,39623,206,929,840
159,364,199,76015,471,286,56025,140,840,66040,225,345,056
1612,875,774,67022,239,974,43037,711,260,99062,852,101,650
1715,905,368,71028,781,143,38051,021,117,81088,732,378,800
1817,672,631,90033,578,000,61062,359,143,990113,380,261,800
1917,672,631,90035,345,263,80068,923,264,410131,282,408,400
2015,905,368,71033,578,000,61068,923,264,410137,846,528,820
2112,875,774,67028,781,143,38062,359,143,990131,282,408,400
229,364,199,76022,239,974,43051,021,117,810113,380,261,800
236,107,086,80015,471,286,56037,711,260,99088,732,378,800
243,562,467,3009,669,554,10025,140,840,66062,852,101,650
251,852,482,9965,414,950,29615,084,504,39640,225,345,056
26854,992,1522,707,475,1488,122,425,44423,206,929,840
27348,330,1361,203,322,2883,910,797,43612,033,222,880
28124,403,620472,733,7561,676,056,0445,586,853,480
2938,608,020163,011,640635,745,3962,311,801,440
3010,295,47248,903,492211,915,132847,660,528
312,324,78412,620,25661,523,748273,438,880
32435,8972,760,68115,380,93776,904,685
3366,045501,9423,262,62318,643,560
34777073,815575,7573,838,380
35666843682,251658,008
3637703913991,390
371387419880
38139780
39140
401

RN=41N=42N=43N=44
01111
141424344
2820861903946
310,66011,48012,34113,244
4101,270111,930123,410135,751
5749,398850,668962,5981,086,008
64,496,3885,245,7866,096,4547,059,052
722,481,94026,978,32832,224,11438,320,568
895,548,245118,030,185145,008,513177,232,627
9350,343,565445,891,810563,921,995708,930,508
101,121,099,4081,471,442,9731,917,334,7832,481,256,778
113,159,461,9684,280,561,3765,752,004,3497,669,339,132
127,898,654,92011,058,116,88815,338,678,26421,090,682,613
1317,620,076,36025,518,731,28036,576,848,16851,915,526,432
1435,240,152,72052,860,229,08078,378,960,360114,955,808,528
1563,432,274,89698,672,427,616151,532,656,696229,911,617,056
16103,077,446,706166,509,721,602265,182,149,218416,714,805,914
17151,584,480,450254,661,927,156421,171,648,758686,353,797,976
18202,112,640,600353,697,121,050608,359,048,2061,029,530,696,964
19244,662,670,200446,775,310,800800,472,431,8501,408,831,480,056
20269,128,937,220513,791,607,420960,566,918,2201,761,039,350,070
21269,128,937,220538,257,874,4401,052,049,481,8602,012,616,400,080
22244,662,670,200513,791,607,4201,052,049,481,8602,104,098,963,720
23202,112,640,600446,775,310,800960,566,918,2202,012,616,400,080
24151,584,480,450353,697,121,050800,472,431,8501,761,039,350,070
25103,077,446,706254,661,927,156608,359,048,2061,408,831,480,056
2663,432,274,896166,509,721,602421,171,648,7581,029,530,696,964
2735,240,152,72098,672,427,616265,182,149,218686,353,797,976
2817,620,076,36052,860,229,080151,532,656,696416,714,805,914
297,898,654,92025,518,731,28078,378,960,360229,911,617,056
303,159,461,96811,058,116,88836,576,848,168114,955,808,528
311,121,099,4084,280,561,37615,338,678,26451,915,526,432
32350,343,5651,471,442,9735,752,004,34921,090,682,613
3395,548,245445,891,8101,917,334,7837,669,339,132
3422,481,940118,030,185563,921,9952,481,256,778
354,496,38826,978,328145,008,513708,930,508
36749,3985,245,78632,224,114177,232,627
37101,270850,6686,096,45438,320,568
3810,660111,930962,5987,059,052
3982011,480123,4101,086,008
404186112,341135,751
4114290313,244
42143946
43144
441

RN=45N=46N=47N=48
01111
145464748
2990103510811128
314,19015,18016,21517,296
4148,995163,185178,365194,580
51,221,7591,370,7541,533,9391,712,304
68,145,0609,366,81910,737,57312,271,512
745,379,62053,524,68062,891,49973,629,072
8215,553,195260,932,815314,457,495377,348,994
9886,163,1351,101,716,3301,362,649,1451,677,106,640
103,190,187,2864,076,350,4215,178,066,7516,540,715,896
1110,150,595,91013,340,783,19617,417,133,61722,595,200,368
1228,760,021,74538,910,617,65552,251,400,85169,668,534,468
1373,006,209,045101,766,230,790140,676,848,445192,928,249,296
14166,871,334,960239,877,544,005341,643,774,79582,320,623,240
15344,867,425,584511,738,760,544751,616,304,5491,093,260,079,344
16646,626,422,970991,493,848,5541,503,232,609,0982,254,848,913,647
171,103,068,603,8901,749,695,026,8602,741,188,875,4144,244,421,484,512
181,715,884,494,9402,818,953,098,8304,568,648,125,6907,309,837,001,104
192,438,362,177,0204,154,246,671,9606,973,199,770,79011,541,847,896,480
203,169,870,830,1265,608,233,007,1469,762,479,679,10616,735,679,449,896
213,773,655,750,1506,943,526,580,27612,551,759,587,42222,314,239,266,528
224,116,715,363,8007,890,371,113,95014,833,897,694,22627,385,657,281,648
234,116,715,363,8008,233,430,727,60016,123,801,841,55030,957,699,535,776
243,773,655,750,1507,890,371,113,95016,123,801,841,55032,247,603,683,100
253,169,870,830,1266,943,526,580,27614,833,897,694,22630,957,699,535,776
262,438,362,177,0205,608,233,007,14612,551,759,587,42227,385,657,281,648
271,715,884,494,9404,154,246,671,9609,762,479,679,10622,314,239,266,528
281,103,068,603,8902,818,953,098,8306,973,199,770,79016,735,679,449,896
29646,626,422,9701,749,695,026,8604,568,648,125,69011,541,847,896,480
30344,867,425,584991,493,848,5542,741,188,875,4147,309,837,001,104
31166,871,334,960511,738,760,5441,503,232,609,0984,244,421,484,512
3273,006,209,04539,877,544,005751,616,304,5492,254,848,913,647
3328,760,021,745101,766,230,790341,643,774,7951,093,260,079,344
3410,150,595,91038,910,617,655140,676,848,445482,320,623,240
353,190,187,28613,340,783,19652,251,400,851192,928,249,296
36886,163,1354,076,350,42117,417,133,61769,668,534,468
37215,553,1951,101,716,3305,178,066,75122,595,200,368
3845,379,620260,932,8151,362,649,1456,540,715,896
398,145,06053,524,680314,457,4951,677,106,640
401,221,7599,366,81962,891,499377,348,994
41148,9951,370,75410,737,57373,629,072
4214,190163,1851,533,93912,271,512
4399015,180178,3651,712,304
4445103516,215194,580
45146108117,296
461471128
47148
481

RN=49N=50N=51N=52
01111
149505152
21176122512751326
318,42419,60020,82522,100
4211,876230,300249,900270,725
51,906,8842,118,7602,349,0602,598,960
613,983,81615,890,70018,009,46020,358,520
785,900,58499,884,400115,775,100133,784,560
8450,978,066536,878,650636,763,050752,538,150
92,054,455,6342,505,433,7003,042,312,3503,679,075,400
108,217,822,53610,272,278,17012,777,711,87015,820,024,220
1129,135,916,26437,353,738,80047,626,016,97060,403,728,840
1292,263,734,836121,399,651,100158,753,389,900206,379,406,870
13262,596,783,764354,860,518,600476,260,169,700635,013,559,600
14675,248,872,536937,845,656,3001,292,706,174,9001,768,966,344,600
151,575,580,702,5842,250,829,575,1203,188,675,231,4204,481,381,406,320
163,348,108,992,9914,923,689,695,5757,174,519,270,69510,363,194,502,115
176,499,270,398,1599,847,379,391,15014,771,069,086,72521,945,588,357,420
1811,554,258,485,61618,053,528,883,77527,900,908,274,92542,671,977,361,650
1918,851,684,897,58430,405,943,383,20048,459,472,266,97576,360,380,541,900
2028,277,527,346,37647,129,212,243,96077,535,155,627,160125,994,627,894,135
2139,049,918,716,42467,327,446,062,800114,456,658,306,760191,991,813,933,920
2249,699,896,548,17688,749,815,264,600156,077,261,327,400270,533,919,634,160
2358,343,356,817,424108,043,253,365,600196,793,068,630,200352,870,329,957,600
2463,205,303,218,876121,548,660,036,300229,591,913,401,900426,384,982,032,100
2563,205,303,218,876126,410,606,437,752247,959,266,474,052477,551,179,875,952
2658,343,356,817,424121,548,660,036,300247,959,266,474,052495,918,532,948,104
2749,699,896,548,176108,043,253,365,600229,591,913,401,900477,551,179,875,952
2839,049,918,716,42488,749,815,264,600196,793,068,630,200426,384,982,032,100
2928,277,527,346,37667,327,446,062,800156,077,261,327,400352,870,329,957,600
3018,851,684,897,58447,129,212,243,960114,456,658,306,760270,533,919,634,160
3111,554,258,485,61630,405,943,383,20077,535,155,627,160191,991,813,933,920
326,499,270,398,15918,053,528,883,77548,459,472,266,975125,994,627,894,135
333,348,108,992,9919,847,379,391,15027,900,908,274,92576,360,380,541,900
341,575,580,702,5844,923,689,695,57514,771,069,086,72542,671,977,361,650
35675,248,872,5362,250,829,575,1207,174,519,270,69521,945,588,357,420
36262,596,783,764937,845,656,3003,188,675,231,42010,363,194,502,115
3792,263,734,836354,860,518,6001,292,706,174,9004,481,381,406,320
3829,135,916,264121,399,651,100476,260,169,7001,768,966,344,600
398,217,822,53637,353,738,800158,753,389,900635,013,559,600
402,054,455,63410,272,278,17047,626,016,970206,379,406,870
41450,978,0662,505,433,70012,777,711,87060,403,728,840
4285,900,584536,878,6503,042,312,35015,820,024,220
4313,983,81699,884,400636,763,0503,679,075,400
441,906,88415,890,700115,775,100752,538,150
45211,8762,118,76018,009,460133,784,560
4618,424230,3002,349,06020,358,520
47117619,600249,9002,598,960
4849122520,825270,725
49150127522,100
501511326
51152
521

 Reference 7Z78 Main Top Factorials and Combinations