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The formula counting all functions N → X is not useful here, because the number of them grouped together by permutations of N varies from one function to another. 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 ...
Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers, starting with the 0th triangular number, is
It separates out the sorted and reversed order of a set of items from the other ("mixed") orders, evaluating the number of mixed orders by subtracting two from the usual product formula for the factorial. The product rule for permutations was also described by 6th-century CE Jain monk Jinabhadra. [2]
In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming. [1]The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. [2]
K-pop (/ k eɪ p ɒ p /, Korean: 케이팝; RR: Keipap), short for Korean popular music, [1] is a form of popular music originating in South Korea. [2] It includes styles and genres from around the world, such as pop, hip hop, R&B, rock, jazz, gospel, reggae, electronic dance, folk, country, disco, and classical on top of its traditional Korean music roots. [3]
The number of hospital admissions in Scotland for diseases such as cancer was 2,528 in 2002. Over the next ten years, by 2012, this had increased to 2,669. [215] Hospital admissions for other diseases, such as coronary heart disease (CHD) were lower, with 727 admissions in 2002, and decreasing to 489 in 2012. [215]
Germany, [e] officially the Federal Republic of Germany, [f] is a country in Central Europe.It lies between the Baltic and North Sea to the north and the Alps to the south. Its sixteen constituent states have a total population of over 82 million in an area of 357,596 km 2 (138,069 sq mi), making it the most populous member state of the European Union.
The English name of "Singapore" is an anglicisation of the native Malay name for the country, Singapura (pronounced), which was in turn derived from the Sanskrit word for 'lion city' (Sanskrit: सिंहपुर; romanised: Siṃhapura; Brahmi: 𑀲𑀺𑀁𑀳𑀧𑀼𑀭; literally "lion city"; siṃha means 'lion', pura means 'city' or 'fortress'). [9]