Factorial Notation

Fairly quickly you will find that writing out $1 \times 2 \times \dotsb \times n$ as a whole will become boring and tedious, let alone pressing those silly buttons on a calculator to find the answer!

That’s when the factorial notation comes in! It even has its own calculator button.

In this notation, we write the phrase $$“1 \times 2 \times 3 \times \dotsb \times n”$$ as the phrase $$“n!”$$ Yep. It’s that simple. Note that the exclamation mark does not mean I’m shouting it. The exlamation mark is actually part of the notation.

The key symbol here is the exclamation mark, “!”, after the number, pronounced here as “$n$-factorial”. This would have the meaning of “to multiply every single positive whole number less than and equal to itself”.

For example, $5! = 1 \times 2 \times 3 \times 4 \times 5$, which equals $120$.

You can see that the number of possible arrangements of $n$ distinct objects is $n!$ (that is, $n$-factorial).

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