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In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations).For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange.
The number associated in the combinatorial number system of degree k to a k-combination C is the number of k-combinations strictly less than C in the given ordering. This number can be computed from C = {c k, ..., c 2, c 1} with c k > ... > c 2 > c 1 as follows.
The numbers of compositions of n +1 into k +1 ordered partitions form Pascal's triangle Using the Fibonacci sequence to count the {1, 2}-restricted compositions of n, for example, the number of ways one can ascend a staircase of length n, taking one or two steps at a time
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.
However, you could use the same combination of numbers for every draw, and you may never win a single penny. The Powerball jackpot for Wednesday, Nov 8, at 11:00 pm, is $196 million.
The Stirling numbers of the second kind can represent the total number of rhyme schemes for a poem of n lines. (,) gives the number of possible rhyming schemes for n lines using k unique rhyming syllables. As an example, for a poem of 3 lines, there is 1 rhyme scheme using just one rhyme (aaa), 3 rhyme schemes using two rhymes (aab, aba, abb ...
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number.
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures.It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.