n factorial, denoted as $n!$, is the product of all positive integers from 1 to $n$. It is commonly used in permutations and combinations to count possible arrangements.
5 Must Know Facts For Your Next Test
0! is defined to be 1.
$n!$ grows very rapidly with increasing $n$.
The formula for permutations of $n$ items taken $r$ at a time is $\frac{n!}{(n-r)!}$.
$n!$ can be used to calculate combinations using the formula $\binom{n}{r} = \frac{n!}{r!(n-r)!}$.
In sequences and series, factorials often appear in formulas for terms involving products.
A selection of items without regard to order. The number of combinations of $n$ objects taken $r$ at a time is given by $\binom{n}{r} = \frac{n!}{r!(n-r)!}$.
A coefficient that appears in the binomial theorem, denoted as $\binom{n}{k}$, representing the number of ways to choose $k$ elements from a set of $n$ elements.