Calculating Different Mii Combinations

How many different Mii designs are possible? I started counting the options, did the math, and here are the results.

	Attribute	Options
1	Genders	2
2	Clothing Colors	12
3	Heights	10
4	Weights	10
5	Face Shapes	8
6	Makeup Types	12
7	Skin Colors	6
8	Hair Styles	72
9	Hair Parts	2
10	Hair Colors	8
11	Eyebrows	24
12	Eyebrow Colors	8
13	Eyebrow Vertical Steps	16
14	Eyebrow Size Steps	9
15	Eyebrow Rotation Steps	12
16	Eyebrow Horizontal Steps	13
17	Eye Types	42
18	Eye Colors	6
19	Eye Vertical Steps	19
20	Eye Size Steps	8
21	Eye Rotation Steps	8
22	Eye Horizontal Steps	13
23	Noses	12
24	Nose Vertical Steps	19
25	Nose Sizes	9
26	Lips	24
27	Lips Colors	3
28	Lips Vertical Steps	19
29	Lips Sizes	9
30	Glasses	9
31	Glasses Colors	6
32	Glasses Vertical Steps	21
33	Glasses Sizes	8
34	Mustaches	4
35	Mustache Colors	8
36	Mustache Vertical Steps	17
37	Mustache Sizes	9
38	Moles	2
39	Mole Vertical Steps	31
40	Mole Sizes	9
41	Mole Horizontal Steps	17
42	Goatee Types	4
43	Goatee Colors	8
	Total	568

Exceptions

1 hair style (bald) has no color or part
49 hair styles have no part
1 eyebrow style(none) has no color, vertical step, size, rotation or horizontal step
7 eye types have no color
17 lips have no color
1 glasses type (none) has no color, vertical step, or size
1 mustache type (none) has no color, vertical step, or size
1 mole (none) has no vertical step, size, or horizontal step
1 goatee type (none) has no color

Combinations

To determine the number of distinct combinations I used the formula: 568! / (43! * (568-43)!)

Result

Using Wolfram Alpha to solve 568! / (43! * (568-43)!), we can see that there are 88 vigintillion, 613 novemdecillion, 583 octodecillion, 674 septendecillion, 758 sexdecillion, 947 quindecillion, 813 quattuordecillion, 475 tredecillion, 143 duodecillion, 744 undecillion, 24 decillion, 970 nonillion, 165 octillion, 692 septillion, 788 sextillion, 754 quintillion, 421 quadrillion, 531 trillion, 161 billion, 395 million, 650 thousand and 32 Mii Combinations.