Combinatorics: Rarity of a Trinary Note

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In the previous thread, I had an anon mention that you could figure out the rarity of a trinary note through the following formula: (3/10)^8 I tested this out with solid notes, and I had this problem occur. (1/10)^8 = 1/100,000,000 This would imply that there only exists one type of solid note, when there actually exist ten types of solid notes. I think the more accurate formula for finding the rarity of a trinary note would be (3/10)^7, because (1/10)^7 is 1/10,000,000, and there are 100,000,000 possible serial numbers, so there are ten serial numbers that will be made up of solid digits. Of course, any random serial number is going to be one in a hundred million, or one in 10^8, and not one in 10^7. Let's discuss.