Factorial

This function returns the factorial for the given argument.

The factorial is the product of all natural numbers (without zero) less than or equal to the argument. In the formula, the factorial is indicated by an exclamation mark after the argument.

To calculate, enter a natural number, then click on the 'Calculate' button.

Factorial formula

\(\displaystyle x!= \sum^{x}_{k-1} \)   \(\displaystyle k=1·2·3·4····x\)

Description

In mathematics, the factorial is the function that which assigns to every natural number the product of all positive natural numbers, that do not exceed this number. It is abbreviated with an exclamation mark (“!”) after the function argument.

Factorials play an important role in counting combinatorics because \(n!\) determines the number of ways in which distinguishable objects can be arranged in a row.

For example, there is a competition with six participants \(\displaystyle 6!\) different options for the order at the finish line. All six participants are eligible for first place. Once the first participant has arrived, only five participants can compete for second place. So there are \(6\cdot 5 = 30\) possibilities for the first two places. If second place is also awarded, only four participants will be considered for third place. So \(30\cdot 4 = 120\) possible placements.

Ultimately there is \(\displaystyle 6!=6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1=720 \) different options for reaching the finish line.