Combination
selection of objects where order inst important
In mathematics, a combination is a way of selecting objects from a larger set, where the order of the objects selected does not matter.
In a combination, the number of ways to select r objects from a set of n objects is given by the formula:
nCr = n! / (r!(n-r)!)
where nCr denotes the number of combinations of n objects taken r at a time, n! denotes the factorial of n, r! denotes the factorial of r, and (n-r)! denotes the factorial of (n-r).
For example, if we have a set of 5 objects {a, b, c, d, e} and we want to select 3 objects from this set, the number of combinations of 3 objects taken from this set would be:
5C3 = 5! / (3!(5-3)!) = 10
This means that there are 10 ways to select 3 objects from the set of 5 objects, namely: {a, b, c}, {a, b, d}, {a, b, e}, {a, c, d}, {a, c, e}, {a, d, e}, {b, c, d}, {b, c, e}, {b, d, e}, and {c, d, e}.
Combinations are used in many different areas of mathematics and statistics, including probability, combinatorics, and set theory. They are also commonly used in problems related to counting and permutations.
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