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These combinations (subsets) are enumerated by the 1 digits of the set of base 2 numbers counting from 0 to 2 n − 1, where each digit position is an item from the set of n. Given 3 cards numbered 1 to 3, there are 8 distinct combinations ( subsets ), including the empty set :
The combinations are represented as strictly decreasing sequences c k > ... > c 2 > c 1 ≥ 0 where each c i corresponds to the index of a chosen element in a given k-combination. Distinct numbers correspond to distinct k-combinations, and produce them in lexicographic order. The numbers less than () correspond to all k-combinations of {0, 1 ...
The list of all single-letter-single-digit combinations contains 520 ... A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A-0 A-1 A-2 A-3 A-4 A-5 A-6 A-7 A-8 A-9 B0 B1 B2 B3 B4 B5 B6 B7 ...
The list of all single-letter-double-digit combinations contains 7,800 elements of the form [[{{letter}}{{digit}}{{digit}}]] and [[{{letter}}-{{digit}}{{digit}}]] and ...
All integers are rational, but there are rational numbers that are not integers, such as −2/9. Real numbers (): Numbers that correspond to points along a line. They can be positive, negative, or zero. All rational numbers are real, but the converse is not true. Irrational numbers (): Real numbers that are not rational. Imaginary numbers ...
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Rather, as explained under combinations, the number of n-multicombinations from a set with x elements can be seen to be the same as the number of n-combinations from a set with x + n − 1 elements. This reduces the problem to another one in the twelvefold way, and gives as result
No. 32 appeared most often — 173 times — among the first five balls drawn in winning combinations, followed by the No. 39 in 163 combinations, according to data.