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Why is this first line true: "This works because there are 3876 possible unique values for a set of 4 4 bit values" Each 4 bit number has 16 possible values. A
by rasen58 9y ago
Why is this first line true: "This works because there are 3876 possible unique values for a set of 4 4 bit values"
Each 4 bit number has 16 possible values. And you can order them in the set in 4! = 24 ways. So I thought you would get 24 * 16 = 384. Can someone explain?
- karlding 9y agoThey're taking the multiset [0]. So it's \binom{2^4 + 4 - 1}{4} = 3876 In other words, there are 3876 multisets of cardinality 4 with elements taken from the set containing all 4 bit values. [0] https://en.wikipedia.org/wiki/Multiset https://en.wikipedia.org/wiki/Multiset
- rasen58 9y agoCan you explain the top number (2^4 + 4 - 1)? I understand the bottom number 4 is probably because you're choosing 4 values out of the set of numbers from the top, but not sure how you got 2^4 + 4 - 1.