combination
Sign in to saveIn 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. More formally, a k-combination of a set S is a subset of k distinct elements of S. So, two combinations are identical if and only if each combination has the same members. (The arrangement of the members in each set does not mat
AI overview
A combination is a way of selecting items from a group where the order doesn't matter—for instance, picking an apple and an orange is the same combination as picking an orange and an apple. This concept matters in mathematics because it helps us count and analyze different possible selections, which is useful in probability, statistics, and many real-world problems involving choices and groupings.
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Article
12 sectionsContents
- Number of ''k''-combinations
- Example of counting combinations
- Enumerating ''k''-combinations
- Number of combinations with repetition
- Example of counting multisubsets
- Number of ''k''-combinations for all ''k''
- Probability: sampling a random combination
- Number of ways to put objects into bins
- See also
- Notes
- References
- External links
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. More formally, a k-combination of a set S is a subset of k distinct elements of S. So, two combinations are identical if and only if each combination has the same members. (The arrangement of the members in each set does not matter.) If the set has n elements, the number of k-combinations, denoted by C(n,k) or C^n_k, is equal to the binomial coefficient:
\binom nk = \frac{n(n-1)\dotsb(n-k+1)}{k(k-1)\dotsb1},