Math Help -> Basic Principles -> Factorials, Consecutive Integer Products -> Digit Frequency in n!

How many 1's are there in n!? This question was asked on NRICH, and while I have no way of calculating the answer in the general case, it's not too hard to come up with an answer for a particular n. This table gives the digit frequencies for n!, where n ranges from 1 to 500.

Digit Frequency in n!

n	0's	1's	2's	3's	4's	5's	6's	7's	8's	9's	Total
1	0	1	0	0	0	0	0	0	0	0	1
2	0	0	1	0	0	0	0	0	0	0	1
3	0	0	0	0	0	0	1	0	0	0	1
4	0	0	1	0	1	0	0	0	0	0	2
5	1	1	1	0	0	0	0	0	0	0	3
6	1	0	1	0	0	0	0	1	0	0	3
7	2	0	0	0	1	1	0	0	0	0	4
8	2	0	1	1	1	0	0	0	0	0	5
9	1	0	1	1	0	0	1	0	2	0	6
10	2	0	1	1	0	0	1	0	2	0	7
11	2	1	0	1	0	0	1	0	1	2	8
12	4	1	0	0	1	0	1	1	0	1	9
13	4	0	3	0	0	0	1	1	1	0	10
14	2	2	2	0	0	0	0	2	2	1	11
15	4	1	0	2	1	0	2	2	1	0	13
16	4	0	3	0	0	0	0	1	4	2	14
17	4	0	1	1	1	2	2	1	2	1	15
18	5	0	2	2	1	1	1	3	1	0	16
19	6	3	2	1	2	1	1	0	2	0	18
20	7	1	3	1	2	0	2	1	1	1	19
21	7	3	1	0	3	1	0	2	0	3	20
22	8	2	2	0	1	0	2	6	1	0	22
23	5	1	2	1	2	2	3	2	4	1	23
24	6	1	2	5	4	0	2	1	1	2	24
25	9	4	1	3	2	3	0	0	2	2	26
26	8	3	2	2	3	3	4	0	1	1	27
27	9	3	1	1	2	2	3	1	6	1	29
28	10	4	0	3	4	2	2	1	4	0	30
29	7	4	0	3	3	2	3	3	2	4	31
30	9	3	4	2	1	4	3	0	5	2	33
31	7	2	7	1	1	3	2	4	6	1	34
32	10	5	3	7	0	1	5	1	2	2	36
33	8	7	1	2	3	2	3	1	8	2	37
34	11	2	4	3	4	2	4	2	2	5	39
35	9	4	3	7	3	2	7	2	1	3	41
36	10	4	3	4	3	2	2	4	3	7	42
37	12	4	3	5	3	5	3	3	2	4	44
38	16	7	7	1	3	1	5	4	0	1	45
39	12	3	4	5	3	2	2	4	7	5	47
40	9	6	5	3	4	5	3	4	4	5	48
41	15	6	4	5	3	6	6	3	2	0	50
42	13	6	3	3	6	5	5	3	4	4	52
43	13	4	4	9	2	7	6	4	2	2	53
44	12	6	4	3	5	5	5	4	9	2	55
45	13	7	4	5	4	5	8	4	3	4	57
46	16	4	8	1	3	8	4	1	7	6	58
47	11	10	6	5	3	5	7	2	4	7	60
48	14	4	6	7	4	6	6	8	4	3	62
49	14	5	10	6	3	5	6	5	7	2	63
50	19	7	3	6	7	2	9	5	5	2	65
51	18	10	10	6	3	4	5	3	5	3	67
52	18	3	3	4	5	7	8	8	9	3	68
53	17	2	6	9	7	3	7	5	8	6	70
54	18	5	9	8	6	3	3	7	9	4	72
55	18	5	6	5	6	11	9	4	4	6	74
56	17	4	1	3	13	5	6	9	11	6	75
57	20	7	9	4	8	6	7	4	7	5	77
58	17	10	10	5	8	5	4	4	10	6	79
59	19	6	6	8	7	5	6	7	9	8	81
60	19	8	9	8	10	3	8	7	4	6	82
61	26	3	10	4	4	7	6	6	11	7	84
62	20	8	13	8	4	6	6	8	7	6	86
63	21	9	8	5	8	4	11	8	7	7	88
64	20	12	6	9	10	7	6	3	12	5	90
65	20	5	11	7	8	10	8	9	7	6	91
66	23	5	8	7	16	3	8	8	9	6	93
67	22	8	8	6	10	7	11	6	9	8	95
68	25	11	8	9	7	8	6	8	7	8	97
69	21	9	14	10	13	5	4	8	8	7	99
70	20	7	7	5	6	10	11	9	14	12	101
71	25	6	8	7	5	7	11	10	18	5	102
72	23	6	10	8	10	3	10	12	15	7	104
73	35	16	8	6	7	7	6	7	9	5	106
74	23	13	14	10	7	13	5	7	9	7	108
75	25	9	9	7	13	9	9	9	10	10	110
76	24	7	12	11	11	10	8	9	8	12	112
77	32	7	10	7	11	6	9	7	18	7	114
78	25	11	16	9	10	9	8	10	12	6	116
79	29	15	8	10	4	7	11	10	14	9	117
80	27	8	12	8	13	14	10	9	13	5	119
81	27	9	9	8	13	13	8	14	8	12	121
82	28	13	5	15	16	1	11	11	10	13	123
83	30	10	9	10	10	12	12	12	8	12	125
84	27	15	12	13	8	8	13	9	12	10	127
85	36	13	14	8	15	13	9	7	5	9	129
86	28	8	17	10	14	13	11	13	8	9	131
87	27	14	16	13	10	11	7	17	8	10	133
88	28	14	12	8	18	10	12	2	18	13	135
89	34	12	9	12	6	10	15	11	10	18	137
90	28	11	10	10	13	12	15	12	14	14	139
91	29	12	8	6	12	17	17	19	9	12	141
92	29	13	8	18	17	17	8	15	11	7	143
93	32	16	17	12	12	14	11	12	12	7	145
94	37	11	11	12	12	15	16	10	16	7	147
95	32	8	19	15	12	12	11	15	10	15	149
96	36	9	7	9	16	11	11	15	16	20	150
97	26	17	13	12	11	11	13	16	17	16	152
98	35	6	16	10	16	9	14	19	16	13	154
99	28	15	19	10	10	14	19	7	14	20	156
100	30	15	19	10	10	14	19	7	14	20	158
101	35	10	14	18	14	13	14	12	12	18	160
102	37	12	9	12	17	27	16	6	11	15	162
103	36	16	17	11	18	15	11	9	17	14	164
104	33	13	13	12	16	14	11	25	18	12	167
105	45	11	14	16	11	11	15	15	12	19	169
106	36	11	19	20	22	8	15	15	18	7	171
107	42	19	15	22	11	17	14	10	11	12	173
108	41	17	12	16	17	15	12	12	19	14	175
109	39	13	21	23	17	10	8	15	17	14	177
110	38	18	23	13	18	13	12	19	13	12	179
111	39	17	12	15	18	20	19	19	10	12	181
112	38	10	17	17	15	15	14	22	18	17	183
113	35	26	24	14	15	14	17	15	12	13	185
114	47	19	16	19	19	18	11	8	18	12	187
115	51	19	18	18	12	21	9	12	13	16	189
116	44	23	14	18	8	16	19	13	17	19	191
117	47	15	14	14	25	11	21	14	14	18	193
118	40	13	24	21	17	14	17	13	23	13	195
119	42	16	11	18	29	17	12	20	19	13	197
120	45	19	15	16	15	21	16	11