ID rolling: How likely are you to get a word in your ID?

Length (source: Collins Scrabble Dictionary):
1 letter	2
2 letters	124
3 letters	1292
4 letters	5454
5 letters	12478
6 letters	22157
7 letters	32909
8 letters	40161

Possible combinations:
1 letter	4
2 letters	496
3 letters	10336
4 letters	87264
5 letters	399296
6 letters	1418048
7 letters	4212352
8 letters	10281216

In possible positions:
1 letter	32
2 letters	3472
3 letters	62016
4 letters	349056
5 letters	1197888
6 letters	2836096
7 letters	8424704
8 letters	10281216

Possible number of IDs with 8 characters: 281474976710656
Possible number of IDs with 7 characters: 4398046511104
Possible number of IDs with 6 characters: 68719476736
Possible number of IDs with 5 characters: 1073741824
Possible number of IDs with 4 characters: 16777216
Possible number of IDs with 3 characters: 262144
Possible number of IDs with 2 characters: 4096
Possible number of IDs with 1 characters: 64

Possible number of IDs with x characters multiplied by possible positions of 8-x letter(s):
x=1 - 140737488355328
x=2 - 238594023227392
x=3 - 66589172957184
x=4 - 5856187908096
x=5 - 314019151872
x=6 - 11616649216
x=7 - 539181056
x=8 - 10281216

Percentage chance of getting an ID contain a word that is x letters long:
x=1 - 50%
x=2 - 84.766%
x=3 - 23.657%
x=4 - 2.081%
x=5 - 0.112%
x=6 - 0.00413%
x=7 - 1.916e-6 %
x=8 - 3.653e-8 %