Syntax. FACT(number)
Definition. This function returns the factorial of a number.
Argument
number (required) The nonnegative number for which you want the factorial. If number isn’t an integer, the decimal places are truncated.
Background. The factorial function is used to calculate partial products of natural numbers. The factorial of a number n is the result of the product of all positive integers less than or equal to n.
For example, the factorial of the number 4 is calculated as:
4! = 1 • 2 • 3 • 4 = 24
The formula is:
n! = n • (n – 1) • (n – 2) •...• 3 • 2 • 1
Note that the factorial of zero is defined: 0! = 1.
Example. In combinatorics, factorials are important because n! is the number of possibilities to arrange n discriminable elements.
Assume four runners participate in a marathon. How many different combinations are possible when all runners reach the finish line?
Every of the four runners could make first place. After the first runner passes the finish line, three runners can compete for second place. After the second runner passes the finish line, only two runners are left for third place, and only one runner is left for fourth place. Therefore, 4! = 24 different combinations exist.
The Excel formula is =FACT(4)
Sample Files
Use the FACT worksheet in the Chapter16.xls or Chapter16.xlsx sample file. The sample files are found in the Chapter16 folder. For more information about the sample files, see the section titled Using the Sample Files.
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