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Definition of FactorialLet n be a positive integer. n factorial, written n!, is defined by

n! = 1 * 2 * 3 * ... (n - 1) * n

The special case when n = 0, 0 factorial is given by: 0! = 1

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What is factorial notation?

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What does it mean when a factorial is in a parenthesis?

When a factorial is in parentheses, it typically indicates that the entire expression within the parentheses should be evaluated first before applying the factorial operation. For example, (n!) means to first calculate the value of n and then take the factorial of that value. This notation helps clarify the order of operations in mathematical expressions.


How many permutations are in the word mathematics?

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Why factorial has an exclamation sign?

The exclamation sign in mathematics, used to denote factorial, originates from the Latin word "factorialis," which means "of factors." The symbol was popularized in the 19th century by mathematicians to succinctly represent the product of all positive integers up to a given number. For example, ( n! ) indicates the product of all integers from 1 to ( n ). The exclamation mark thus serves as a concise notation for this specific operation.


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