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'''Permutation''' and '''combination''' are fundamental concepts in combinatorics, a branch of mathematics that deals with counting, arranging, and selecting objects. These concepts are used to solve problems related to arrangements and selections of elements from a given set.
'''Permutation:'''
A permutation is an arrangement of objects in a specific order.
The number of permutations of a set of n distinct objects taken r at a time is denoted by P(n, r) and is given by the formula:
P(n, r) = 𝑛!/(𝑛−𝑟)!
where n! (read as "n factorial") is the product of all positive integers up to n.
Permutations can be with or without replacement. With replacement means an element can be chosen more than once, while without replacement means once an element is chosen, it cannot be chosen again.
'''Combination:'''
A combination is a selection of objects without considering the order.
The number of combinations of a set of n distinct objects taken r at a time is denoted by C(n, r) and is given by the formula:
C(n, r) = 𝑛!/𝑟!(𝑛−𝑟)!
The key difference between permutations and combinations is that in permutations, the order matters, while in combinations, it does not.
Combinations are often used when the selection is made without distinguishing between the chosen elements.
Understanding permutations and combinations is essential in solving a wide range of problems in mathematics and real-world situations where counting and arrangement are involved.
'''Combinations and permutations''' in the mathematical sense are described in several articles.
Described together, in-depth:
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