What Permutation is
Permutation is a mathematical process of arranging a set of items in a certain order or combination. It is used to calculate the number of possible arrangements of a given set of items.
Steps for Permutation:
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Count the number of items in the set: Permutation is all about arranging a set of items in a certain order or combination, thus the first step is to count the number of items in the set.
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Calculate the number of possible arrangements: Once you have the number of items in the set, calculate the total number of possible arrangements of the set. This can be done by using the formula n!, where n is the number of items in the set.
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Select a particular arrangement: Now, you need to select a particular arrangement from the total number of possible arrangements.
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Calculate the number of permutations: After selecting a particular arrangement, calculate the number of permutations for the given set of items by using the formula P(n,r) = n! / (n-r)! , where n is the number of items in the set and r is the number of items in the particular arrangement.
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Determine the permutation: Finally, determine the permutation of the given set by using the formula P(n,r).
Examples
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Permutations can be used to calculate the probability of different outcomes in a series of independent events. For example, permutations can be used to calculate the probability of rolling a certain number with a six-sided die.
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Permutations can be used to calculate the probability of different combinations of outcomes in a series of dependent events. For example, permutations can be used to calculate the probability of different poker hands in a game of Texas Hold ‘Em.
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Permutations can be used to calculate the probability of different rankings of outcomes in a series of mixed events. For example, permutations can be used to calculate the probability of different rankings of a race between three horses.