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.

N	N Factorial (N!)
0	1
1	1
2	2
3	6
4	24
5	120
6	720
7	5040
8	40,320
9	362,880
10	3,628,800
11	39,916,800
12	479,001,600
13	6,227,020,800
14	87,178,291,200
15	1,307,674,368,000
16	20,922,789,888,000
17	355,687,428,096,000
18	6,402,373,705,728,000
19	121,645,100,408,832,000
20	2,432,902,008,176,640,000
21	51,090,942,171,709,440,000
22	1,124,000,727,777,607,680,000
23	25,852,016,738,884,976,640,000
24	620,448,401,733,239,439,360,000
25	15,511,210,043,330,985,984,000,000
26	403,291,461,126,605,635,584,000,000
27	10,888,869,450,418,352,160,768,000,000
28	304,888,344,611,713,860,501,504,000,000
29	8,841,761,993,739,701,954,543,616,000,000
30	265,252,859,812,191,058,636,308,480,000,000
31	8,222,838,654,177,922,817,725,562,880,000,000
32	263,130,836,933,693,530,167,218,012,160,000,000
33	8,683,317,618,811,886,495,518,194,401,280,000,000
34	295,232,799,039,604,140,847,618,609,643,520,000,000
35	10,333,147,966,386,144,929,666,651,337,523,200,000,000
36	371,993,326,789,901,217,467,999,448,150,835,200,000,000
37	13,763,753,091,226,345,046,315,979,581,580,902,400,000,000
38	523,022,617,466,601,111,760,007,224,100,074,291,200,000,000
39	20,397,882,081,197,443,358,640,281,739,902,897,356,800,000,000
40	815,915,283,247,897,734,345,611,269,596,115,894,272,000,000,000
41	33,452,526,613,163,807,108,170,062,053,440,751,665,152,000,000,000
42	1,405,006,117,752,879,898,543,142,606,244,511,569,936,384,000,000,000
43	60,415,263,063,373,835,637,355,132,068,513,997,507,264,512,000,000,000
44	2,658,271,574,788,448,768,043,625,811,014,615,890,319,638,528,000,000,000
45	119,622,220,865,480,194,561,963,161,495,657,715,064,383,733,760,000,000,000
46	5,502,622,159,812,088,949,850,305,428,800,254,892,961,651,752,960,000,000,000
47	258,623,241,511,168,180,642,964,355,153,611,979,969,197,632,389,120,000,000,000
48	12,413,915,592,536,072,670,862,289,047,373,375,038,521,486,354,677,760,000,000,000
49	608,281,864,034,267,560,872,252,163,321,295,376,887,552,831,379,210,240,000,000,000
50	30,414,093,201,713,378,043,612,608,166,064,768,844,377,641,568,960,512,000,000,000,000
51	1,551,118,753,287,382,280,224,243,016,469,303,211,063,259,720,016,986,112,000,000,000,000
52	80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000

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.

R	N=1	N=2	N=3	N=4
0	1	1	1	1
1	1	2	3	4
2		1	3	6
3			1	4
4				1

R	N=5	N=6	N=7	N=8
0	1	1	1	1
1	5	6	7	8
2	10	15	21	28
3	10	20	35	56
4	5	15	35	70
5	1	6	21	56
6		1	7	28
7			1	8
8				1

R	N=9	N=10	N=11	N=12
0	1	1	1	1
1	9	10	11	12
2	36	45	55	66
3	84	120	165	220
4	126	210	330	495
5	126	252	462	792
6	84	210	462	924
7	36	120	330	792
8	9	45	165	495
9	1	10	55	220
10		1	11	66
11			1	12
12				1

R	N=13	N=14	N=15	N=16
0	1	1	1	1
1	13	14	15	16
2	78	91	105	120
3	286	364	455	560
4	715	1001	1365	1820
5	1287	2002	3003	4368
6	1716	3003	5005	8008
7	1716	3432	6435	11,440
8	1287	3003	6435	12,870
9	715	2002	5005	11,440
10	286	1001	3003	8008
11	78	364	1365	4368
12	13	91	455	1820
13	1	14	105	560
14		1	15	120
15			1	16
16				1

R	N=17	N=18	N=19	N=20
0	1	1	1	1
1	17	18	19	20
2	136	153	171	190
3	680	816	969	1140
4	2380	3060	3876	4845
5	6188	8568	11,628	15,504
6	12,376	18,564	27,132	38,760
7	19,448	31,824	50,388	77,520
8	24,310	43,758	75,582	125,970
9	24,310	48,620	92,378	167,960
10	19,448	43,758	92,378	184,756
11	12,376	31,824	75,582	167,960
12	6188	18,564	50,388	125,970
13	2380	8568	27,132	77,520
14	680	3060	11,628	38,760
15	136	816	3876	15,504
16	17	153	969	4845
17	1	18	171	1140
18		1	19	190
19			1	20
20				1

R	N=21	N=22	N=23	N=24
0	1	1	1	1
1	21	22	23	24
2	210	231	253	276
3	1330	1540	1771	2024
4	5985	7315	8855	10,626
5	20,349	26,334	33,649	42,504
6	54,264	74,613	100,947	134,596
7	116,280	170,544	245,157	346,104
8	203,490	319,770	490,314	735,471
9	293,930	497,420	817,190	1,307,504
10	352,716	646,646	1,144,066	1,961,256
11	352,716	705,432	1,352,078	2,496,144
12	293,930	646,646	1,352,078	2,704,156
13	203,490	497,420	1,144,066	2,496,144
14	116,280	319,770	817,190	1,961,256
15	54,264	170,544	490,314	1,307,504
16	20,349	74,613	245,157	735,471
17	5985	26,334	100,947	346,104
18	1330	7315	33,649	134,596
19	210	1540	8855	42,504
20	21	231	1771	10,626
21	1	22	253	2024
22		1	23	276
23			1	24
24				1

R	N=25	N=26	N=27	N=28
0	1	1	1	1
1	25	26	27	28
2	300	325	351	378
3	2300	2600	2925	3276
4	12,650	14,950	17,550	20,475
5	53,130	65,780	80,730	98,280
6	177,100	230,230	296,010	376,740
7	480,700	657,800	888,030	1,184,040
8	1,081,575	1,562,275	2,220,075	3,108,105
9	2,042,975	3,124,550	4,686,825	6,906,900
10	3,268,760	5,311,735	8,436,285	13,123,110
11	4,457,400	7,726,160	13,037,895	21,474,180
12	5,200,300	9,657,700	17,383,860	30,421,755
13	5,200,300	10,400,600	20,058,300	37,442,160
14	4,457,400	9,657,700	20,058,300	40,116,600
15	3,268,760	7,726,160	17,383,860	37,442,160
16	2,042,975	5,311,735	13,037,895	30,421,755
17	1,081,575	3,124,550	8,436,285	21,474,180
18	480,700	1,562,275	4,686,825	13,123,110
19	177,100	657,800	2,220,075	6,906,900
20	53,130	230,230	888,030	3,108,105
21	12,650	65,780	296,010	1,184,040
22	2300	14,950	80,730	376,740
23	300	2600	17,550	98,280
24	25	325	2925	20,475
25	1	26	351	3276
26		1	27	378
27			1	28
28				1

R	N=29	N=30	N=31	N=32
0	1	1	1	1
1	29	30	31	32
2	406	435	465	496
3	3654	4060	4495	4960
4	23,751	27,405	31,465	35,960
5	118,755	142,506	169,911	201,376
6	475,020	593,775	736,281	906,192
7	1,560,780	2,035,800	2,629,575	3,365,856
8	4,292,145	5,852,925	7,888,725	10,518,300
9	10,015,005	14,307,150	20,160,075	28,048,800
10	20,030,010	30,045,015	44,352,165	64,512,240
11	34,597,290	54,627,300	84,672,315	129,024,480
12	51,895,935	86,493,225	141,120,525	225,792,840
13	67,863,915	119,759,850	206,253,075	347,373,600
14	77,558,760	145,422,675	265,182,525	471,435,600
15	77,558,760	155,117,520	300,540,195	565,722,720
16	67,863,915	145,422,675	300,540,195	601,080,390
17	51,895,935	119,759,850	265,182,525	565,722,720
18	34,597,290	86,493,225	206,253,075	471,435,600
19	20,030,010	54,627,300	141,120,525	347,373,600
20	10,015,005	30,045,015	84,672,315	225,792,840
21	4,292,145	14,307,150	44,352,165	129,024,480
22	1,560,780	5,852,925	20,160,075	64,512,240
23	475,020	2,035,800	7,888,725	28,048,800
24	118,755	593,775	2,629,575	10,518,300
25	23,751	142,506	736,281	3,365,856
26	3654	27,405	169,911	906,192
27	406	4060	31,465	201,376
28	29	435	4495	35,960
29	1	30	465	4960
30		1	31	496
31			1	32
32				1

R	N=33	N=34	N=35	N=36
0	1	1	1	1
1	33	34	35	36
2	528	561	595	630
3	5456	5984	6545	7140
4	40,920	46,376	52,360	58,905
5	237,336	278,256	324,632	376,992
6	1,107,568	1,344,904	1,623,160	1,947,792
7	4,272,048	5,379,616	6,724,520	8,347,680
8	13,884,156	18,156,204	23,535,820	30,260,340
9	38,567,100	52,451,256	70,607,460	94,143,280
10	92,561,040	131,128,140	183,579,396	254,186,856
11	193,536,720	286,097,760	417,225,900	600,805,296
12	354,817,320	548,354,040	834,451,800	1,251,677,700
13	573,166,440	927,983,760	1,476,337,800	2,310,789,600
14	818,809,200	1,391,975,640	2,319,959,400	3,796,297,200
15	1,037,158,320	1,855,967,520	3,247,943,160	5,567,902,560
16	1,166,803,110	2,203,961,430	4,059,928,950	7,307,872,110
17	1,166,803,110	2,333,606,220	4,537,567,650	8,597,496,600
18	1,037,158,320	2,203,961,430	4,537,567,650	9,075,135,300
19	818,809,200	1,855,967,520	4,059,928,950	8,597,496,600
20	573,166,440	1,391,975,640	3,247,943,160	7,307,872,110
21	354,817,320	927,983,760	2,319,959,400	5,567,902,560
22	193,536,720	548,354,040	1,476,337,800	3,796,297,200
23	92,561,040	286,097,760	834,451,800	2,310,789,600
24	38,567,100	131,128,140	417,225,900	1,251,677,700
25	13,884,156	52,451,256	183,579,396	600,805,296
26	4,272,048	18,156,204	70,607,460	254,186,856
27	1,107,568	5,379,616	23,535,820	94,143,280
28	237,336	1,344,904	6,724,520	30,260,340
29	40,920	278,256	1,623,160	8,347,680
30	5456	46,376	324,632	1,947,792
31	528	5984	52,360	376,992
32	33	561	6545	58,905
33	1	34	595	7140
34		1	35	630
35			1	36
36				1

R	N=37	N=38	N=39	N=40
0	1	1	1	1
1	37	38	39	40
2	666	703	741	780
3	7770	8436	9139	9880
4	66,045	73,815	82,251	91,390
5	435,897	501,942	575,757	658,008
6	2,324,784	2,760,681	3,262,623	3,838,380
7	10,295,472	12,620,256	15,380,937	18,643,560
8	38,608,020	48,903,492	61,523,748	76,904,685
9	124,403,620	163,011,640	211,915,132	273,438,880
10	348,330,136	472,733,756	635,745,396	847,660,528
11	854,992,152	1,203,322,288	1,676,056,044	2,311,801,440
12	1,852,482,996	2,707,475,148	3,910,797,436	5,586,853,480
13	3,562,467,300	5,414,950,296	8,122,425,444	12,033,222,880
14	6,107,086,800	9,669,554,100	15,084,504,396	23,206,929,840
15	9,364,199,760	15,471,286,560	25,140,840,660	40,225,345,056
16	12,875,774,670	22,239,974,430	37,711,260,990	62,852,101,650
17	15,905,368,710	28,781,143,380	51,021,117,810	88,732,378,800
18	17,672,631,900	33,578,000,610	62,359,143,990	113,380,261,800
19	17,672,631,900	35,345,263,800	68,923,264,410	131,282,408,400
20	15,905,368,710	33,578,000,610	68,923,264,410	137,846,528,820
21	12,875,774,670	28,781,143,380	62,359,143,990	131,282,408,400
22	9,364,199,760	22,239,974,430	51,021,117,810	113,380,261,800
23	6,107,086,800	15,471,286,560	37,711,260,990	88,732,378,800
24	3,562,467,300	9,669,554,100	25,140,840,660	62,852,101,650
25	1,852,482,996	5,414,950,296	15,084,504,396	40,225,345,056
26	854,992,152	2,707,475,148	8,122,425,444	23,206,929,840
27	348,330,136	1,203,322,288	3,910,797,436	12,033,222,880
28	124,403,620	472,733,756	1,676,056,044	5,586,853,480
29	38,608,020	163,011,640	635,745,396	2,311,801,440
30	10,295,472	48,903,492	211,915,132	847,660,528
31	2,324,784	12,620,256	61,523,748	273,438,880
32	435,897	2,760,681	15,380,937	76,904,685
33	66,045	501,942	3,262,623	18,643,560
34	7770	73,815	575,757	3,838,380
35	666	8436	82,251	658,008
36	37	703	9139	91,390
37	1	38	741	9880
38		1	39	780
39			1	40
40				1

R	N=41	N=42	N=43	N=44
0	1	1	1	1
1	41	42	43	44
2	820	861	903	946
3	10,660	11,480	12,341	13,244
4	101,270	111,930	123,410	135,751
5	749,398	850,668	962,598	1,086,008
6	4,496,388	5,245,786	6,096,454	7,059,052
7	22,481,940	26,978,328	32,224,114	38,320,568
8	95,548,245	118,030,185	145,008,513	177,232,627
9	350,343,565	445,891,810	563,921,995	708,930,508
10	1,121,099,408	1,471,442,973	1,917,334,783	2,481,256,778
11	3,159,461,968	4,280,561,376	5,752,004,349	7,669,339,132
12	7,898,654,920	11,058,116,888	15,338,678,264	21,090,682,613
13	17,620,076,360	25,518,731,280	36,576,848,168	51,915,526,432
14	35,240,152,720	52,860,229,080	78,378,960,360	114,955,808,528
15	63,432,274,896	98,672,427,616	151,532,656,696	229,911,617,056
16	103,077,446,706	166,509,721,602	265,182,149,218	416,714,805,914
17	151,584,480,450	254,661,927,156	421,171,648,758	686,353,797,976
18	202,112,640,600	353,697,121,050	608,359,048,206	1,029,530,696,964
19	244,662,670,200	446,775,310,800	800,472,431,850	1,408,831,480,056
20	269,128,937,220	513,791,607,420	960,566,918,220	1,761,039,350,070
21	269,128,937,220	538,257,874,440	1,052,049,481,860	2,012,616,400,080
22	244,662,670,200	513,791,607,420	1,052,049,481,860	2,104,098,963,720
23	202,112,640,600	446,775,310,800	960,566,918,220	2,012,616,400,080
24	151,584,480,450	353,697,121,050	800,472,431,850	1,761,039,350,070
25	103,077,446,706	254,661,927,156	608,359,048,206	1,408,831,480,056
26	63,432,274,896	166,509,721,602	421,171,648,758	1,029,530,696,964
27	35,240,152,720	98,672,427,616	265,182,149,218	686,353,797,976
28	17,620,076,360	52,860,229,080	151,532,656,696	416,714,805,914
29	7,898,654,920	25,518,731,280	78,378,960,360	229,911,617,056
30	3,159,461,968	11,058,116,888	36,576,848,168	114,955,808,528
31	1,121,099,408	4,280,561,376	15,338,678,264	51,915,526,432
32	350,343,565	1,471,442,973	5,752,004,349	21,090,682,613
33	95,548,245	445,891,810	1,917,334,783	7,669,339,132
34	22,481,940	118,030,185	563,921,995	2,481,256,778
35	4,496,388	26,978,328	145,008,513	708,930,508
36	749,398	5,245,786	32,224,114	177,232,627
37	101,270	850,668	6,096,454	38,320,568
38	10,660	111,930	962,598	7,059,052
39	820	11,480	123,410	1,086,008
40	41	861	12,341	135,751
41	1	42	903	13,244
42		1	43	946
43			1	44
44				1

R	N=45	N=46	N=47	N=48
0	1	1	1	1
1	45	46	47	48
2	990	1035	1081	1128
3	14,190	15,180	16,215	17,296
4	148,995	163,185	178,365	194,580
5	1,221,759	1,370,754	1,533,939	1,712,304
6	8,145,060	9,366,819	10,737,573	12,271,512
7	45,379,620	53,524,680	62,891,499	73,629,072
8	215,553,195	260,932,815	314,457,495	377,348,994
9	886,163,135	1,101,716,330	1,362,649,145	1,677,106,640
10	3,190,187,286	4,076,350,421	5,178,066,751	6,540,715,896
11	10,150,595,910	13,340,783,196	17,417,133,617	22,595,200,368
12	28,760,021,745	38,910,617,655	52,251,400,851	69,668,534,468
13	73,006,209,045	101,766,230,790	140,676,848,445	192,928,249,296
14	166,871,334,960	239,877,544,005	341,643,774,795	82,320,623,240
15	344,867,425,584	511,738,760,544	751,616,304,549	1,093,260,079,344
16	646,626,422,970	991,493,848,554	1,503,232,609,098	2,254,848,913,647
17	1,103,068,603,890	1,749,695,026,860	2,741,188,875,414	4,244,421,484,512
18	1,715,884,494,940	2,818,953,098,830	4,568,648,125,690	7,309,837,001,104
19	2,438,362,177,020	4,154,246,671,960	6,973,199,770,790	11,541,847,896,480
20	3,169,870,830,126	5,608,233,007,146	9,762,479,679,106	16,735,679,449,896
21	3,773,655,750,150	6,943,526,580,276	12,551,759,587,422	22,314,239,266,528
22	4,116,715,363,800	7,890,371,113,950	14,833,897,694,226	27,385,657,281,648
23	4,116,715,363,800	8,233,430,727,600	16,123,801,841,550	30,957,699,535,776
24	3,773,655,750,150	7,890,371,113,950	16,123,801,841,550	32,247,603,683,100
25	3,169,870,830,126	6,943,526,580,276	14,833,897,694,226	30,957,699,535,776
26	2,438,362,177,020	5,608,233,007,146	12,551,759,587,422	27,385,657,281,648
27	1,715,884,494,940	4,154,246,671,960	9,762,479,679,106	22,314,239,266,528
28	1,103,068,603,890	2,818,953,098,830	6,973,199,770,790	16,735,679,449,896
29	646,626,422,970	1,749,695,026,860	4,568,648,125,690	11,541,847,896,480
30	344,867,425,584	991,493,848,554	2,741,188,875,414	7,309,837,001,104
31	166,871,334,960	511,738,760,544	1,503,232,609,098	4,244,421,484,512
32	73,006,209,045	39,877,544,005	751,616,304,549	2,254,848,913,647
33	28,760,021,745	101,766,230,790	341,643,774,795	1,093,260,079,344
34	10,150,595,910	38,910,617,655	140,676,848,445	482,320,623,240
35	3,190,187,286	13,340,783,196	52,251,400,851	192,928,249,296
36	886,163,135	4,076,350,421	17,417,133,617	69,668,534,468
37	215,553,195	1,101,716,330	5,178,066,751	22,595,200,368
38	45,379,620	260,932,815	1,362,649,145	6,540,715,896
39	8,145,060	53,524,680	314,457,495	1,677,106,640
40	1,221,759	9,366,819	62,891,499	377,348,994
41	148,995	1,370,754	10,737,573	73,629,072
42	14,190	163,185	1,533,939	12,271,512
43	990	15,180	178,365	1,712,304
44	45	1035	16,215	194,580
45	1	46	1081	17,296
46		1	47	1128
47			1	48
48				1

R	N=49	N=50	N=51	N=52
0	1	1	1	1
1	49	50	51	52
2	1176	1225	1275	1326
3	18,424	19,600	20,825	22,100
4	211,876	230,300	249,900	270,725
5	1,906,884	2,118,760	2,349,060	2,598,960
6	13,983,816	15,890,700	18,009,460	20,358,520
7	85,900,584	99,884,400	115,775,100	133,784,560
8	450,978,066	536,878,650	636,763,050	752,538,150
9	2,054,455,634	2,505,433,700	3,042,312,350	3,679,075,400
10	8,217,822,536	10,272,278,170	12,777,711,870	15,820,024,220
11	29,135,916,264	37,353,738,800	47,626,016,970	60,403,728,840
12	92,263,734,836	121,399,651,100	158,753,389,900	206,379,406,870
13	262,596,783,764	354,860,518,600	476,260,169,700	635,013,559,600
14	675,248,872,536	937,845,656,300	1,292,706,174,900	1,768,966,344,600
15	1,575,580,702,584	2,250,829,575,120	3,188,675,231,420	4,481,381,406,320
16	3,348,108,992,991	4,923,689,695,575	7,174,519,270,695	10,363,194,502,115
17	6,499,270,398,159	9,847,379,391,150	14,771,069,086,725	21,945,588,357,420
18	11,554,258,485,616	18,053,528,883,775	27,900,908,274,925	42,671,977,361,650
19	18,851,684,897,584	30,405,943,383,200	48,459,472,266,975	76,360,380,541,900
20	28,277,527,346,376	47,129,212,243,960	77,535,155,627,160	125,994,627,894,135
21	39,049,918,716,424	67,327,446,062,800	114,456,658,306,760	191,991,813,933,920
22	49,699,896,548,176	88,749,815,264,600	156,077,261,327,400	270,533,919,634,160
23	58,343,356,817,424	108,043,253,365,600	196,793,068,630,200	352,870,329,957,600
24	63,205,303,218,876	121,548,660,036,300	229,591,913,401,900	426,384,982,032,100
25	63,205,303,218,876	126,410,606,437,752	247,959,266,474,052	477,551,179,875,952
26	58,343,356,817,424	121,548,660,036,300	247,959,266,474,052	495,918,532,948,104
27	49,699,896,548,176	108,043,253,365,600	229,591,913,401,900	477,551,179,875,952
28	39,049,918,716,424	88,749,815,264,600	196,793,068,630,200	426,384,982,032,100
29	28,277,527,346,376	67,327,446,062,800	156,077,261,327,400	352,870,329,957,600
30	18,851,684,897,584	47,129,212,243,960	114,456,658,306,760	270,533,919,634,160
31	11,554,258,485,616	30,405,943,383,200	77,535,155,627,160	191,991,813,933,920
32	6,499,270,398,159	18,053,528,883,775	48,459,472,266,975	125,994,627,894,135
33	3,348,108,992,991	9,847,379,391,150	27,900,908,274,925	76,360,380,541,900
34	1,575,580,702,584	4,923,689,695,575	14,771,069,086,725	42,671,977,361,650
35	675,248,872,536	2,250,829,575,120	7,174,519,270,695	21,945,588,357,420
36	262,596,783,764	937,845,656,300	3,188,675,231,420	10,363,194,502,115
37	92,263,734,836	354,860,518,600	1,292,706,174,900	4,481,381,406,320
38	29,135,916,264	121,399,651,100	476,260,169,700	1,768,966,344,600
39	8,217,822,536	37,353,738,800	158,753,389,900	635,013,559,600
40	2,054,455,634	10,272,278,170	47,626,016,970	206,379,406,870
41	450,978,066	2,505,433,700	12,777,711,870	60,403,728,840
42	85,900,584	536,878,650	3,042,312,350	15,820,024,220
43	13,983,816	99,884,400	636,763,050	3,679,075,400
44	1,906,884	15,890,700	115,775,100	752,538,150
45	211,876	2,118,760	18,009,460	133,784,560
46	18,424	230,300	2,349,060	20,358,520
47	1176	19,600	249,900	2,598,960
48	49	1225	20,825	270,725
49	1	50	1275	22,100
50		1	51	1326
51			1	52
52				1

Reference 7Z78 Main

Top Factorials and Combinations

© 2003 Richard Pavlicek