# binomial coefficent equation.

• Sep 25th 2010, 06:43 AM
integral
binomial coefficent equation.
I was watching a video playlist on applications of binomial coefficents and at the end of one of the videos it asked me to make an equation for them.
This is what I got:

$\begin{pmatrix}
n \\
r
\end{pmatrix}=\frac{1}{r!}}\prod_{i=0}^{r-1}(n-i)$

Reasoning: n choose r.
say you have n people and you choose r, you at first have n people to choose from, then you have n-1 people to choose from, then n-2 people to choose from all the way to n-(r-1) because you start with n-0. But you have r! ways to arrange each group of people, so n(n-1)(n-2)...(n-(r-1)) also counts that r! ways to arrange each group of people. So we divide by r!

leaving
$\begin{pmatrix}
n \\
r
\end{pmatrix}=\frac{1}{r!}}\prod_{i=0}^{r-1}(n-i)$

This is correct? (Happy)
• Sep 25th 2010, 12:25 PM
emakarov
Yes.