This page contains numbers appearing in combinatorics, which don’t fit on other lists.

## List of numbers appearing in combinatorics Edit

- In the Gregorian calendar, there are
**217**combinations of day of the week and day in the month, Friday the 13th being the most (in)famous. - Article 79 of the Basic Law for the Federal Republic of Germany requires constitutional amendments to be approved by an absolute two-thirds majority of the Bundestag along with a simple two-thirds majority of the Bundesrat. Article 51 of the same law gives each state at least three votes, a fourth vote for states with more than 2 million inhabitants, a fifth vote for states with more than 6 million inhabitants, and a sixth vote for states with more than 7 million inhabitants. There are currently four states with three votes, seven states with four votes, one state with five votes, and four states with six votes. A calculation reveals that of the 65,536 possible voting patterns,
**7,228**lead to an absolute two-thirds majority. - The number
**7,825**is the smallest natural number*n*for which the set {1, 2, 3, … ,*n*} cannot be written as a union of two disjoint sets, such that both of them contain no Pythagorean triples.^{[1]} - The Kubo character has 11,007 possible mouth expressions and 4,429 possible brow expressions, and therefore 11,007×4,429 =
**48,750,003**possible facial expressions.

## Edit

**405**is the sum of all the numbers on a 9×9 Sudoku grid. It is equal to 9×T_{9}, where T_{n}is the nth triangular number. This number is also called Ternary-dust mite.**6,670,903,752,021,072,936,960**is a combinatoric number equal to the number of possible 9×9 Sudoku grids.^{[2]}- 6,670,903,752,021,072,936,960 is roughly equal to \(f_2(66)\) in the fast-growing hierarchy.

**109,110,688,415,571,316,480,344,899,355,894,085,582,848,000,000,000**is the product of all the numbers on a 9×9 Sudoku grid. It is equal to 1^{9}×2^{9}×3^{9}×4^{9}×5^{9}×6^{9}×7^{9}×8^{9}×9^{9}, the product of the first 9 9th powers.