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Combinations
Combinations Combinations are a method of selecting a subset of elements from a set without regard to the order of selection. This means that different subs...
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Combinations Combinations are a method of selecting a subset of elements from a set without regard to the order of selection. This means that different subs...
Combinations
Combinations are a method of selecting a subset of elements from a set without regard to the order of selection. This means that different subsets can contain the same elements, and the order in which the elements are selected does not matter.
For example, if we have a set of 6 elements, {1, 2, 3, 4, 5, 6}, there are 15 different subsets of this set. Some of these subsets include the elements {1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 2, 6}, {1, 3, 4}, {1, 3, 5}, {1, 3, 6}, {2, 3, 4}, {2, 3, 5}, {2, 3, 6}, {3, 4, 5}, {3, 4, 6}, {4, 5, 6}.
The number of combinations of n elements from a set with n elements is given by the formula n!/(n - r)!, where n! is the factorial of n and (n - r)! is the factorial of (n - r).
For example, if we have a set of 6 elements and we choose 3 elements for a combination, the number of combinations is 6!/(6 - 3)! = 20.
Combinations can be used to solve a variety of problems, such as finding the number of different ways to choose a committee of 5 people from a group of 10 people, or finding the number of different ways to choose a team of 3 players from a group of 10 players