Calculating Different Mii Combinations March 3, 2010

On November 19th 2006, I set out with a friend to buy a Wii on launch day. After futilely showing up at about five stores, we took a chance at this small electronic boutique with ten people waiting outside. After getting into line at eleventh place, I was hearing murmurs of this place only having ten Wiis. We decided to wait the hour and a half and hope for an extra Wii. Five minutes to 11:00 am, this girl that was second in line with her boyfriend decided she was hungry and went to get a bite. Much to my surprise, when the guy came out of the store to tag who would get a Wii, she wasn't there and I got the tenth and last Wii they had.

Since then, I rarely play games on it. I finished Twilight Princess, perfected my power serve in Wii Sports Tennis, and made my share of Miis. Though, this will change a bit when World of Goo releases. Recently, after browsing the Check Mii Out Channel, I started thinking: How many different Mii designs are possible? I started counting the options, did the math, and here are the results.

Options

AttributeOptions
1Genders2
2Clothing Colors12
3Heights10
4Weights10
5Face Shapes8
6Makeup Types12
7Skin Colors6
8Hair Styles72
9Hair Parts2
10Hair Colors8
11Eyebrows24
12Eyebrow Colors8
13Eyebrow Vertical Steps16
14Eyebrow Size Steps9
15Eyebrow Rotation Steps12
16Eyebrow Horizontal Steps13
17Eye Types42
18Eye Colors6
19Eye Vertical Steps19
20Eye Size Steps8
21Eye Rotation Steps8
22Eye Horizontal Steps13
23Noses12
24Nose Vertical Steps19
25Nose Sizes9
26Lips24
27Lips Colors3
28Lips Vertical Steps19
29Lips Sizes9
30Glasses9
31Glasses Colors6
32Glasses Vertical Steps21
33Glasses Sizes8
34Mustaches4
35Mustache Colors8
36Mustache Vertical Steps17
37Mustache Sizes9
38Moles2
39Mole Vertical Steps31
40Mole Sizes9
41Mole Horizontal Steps17
42Goatee Types4
43Goatee Colors8
Total568

Exceptions

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.