I cannot recall what the large () brackets mean - Google seems to be full of links on how to create them but not what they actually are or how to resolve them.
$ \left( \begin{array}{l} n\\ 2 \end{array} \right)r^2 $
Can someone please clarify? In this instance n = 6 and r = 0.05 if that helps.
The binomial coefficient
$$\binom{n}{k} = \frac{n!}{k!(n - k)!}$$
is the number of ways of selecting $k$ elements from $n$ elements when order does not matter (the number of subsets with $k$ elements in an $n$ element set).
The number $n!$, read "$n$ factorial," is defined recursively as follows:
If you substitute $1$ in the definition for $n!$, you obtain
\begin{align*} 1! & = 1(1 - 1)!\\ 1 & = 1 \cdot 0!\\ 1 & = 0! \end{align*}
For positive integers, $n!$ is the product of the first $n$ positive integers. For instance,
\begin{align*} 6! & = 6 \cdot 5!\\ & = 6 \cdot 5 \cdot 4!\\ & = 6 \cdot 5 \cdot 4 \cdot 3!\\ & = 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!\\ & = 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1!\\ & = 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 \end{align*}
Hence,
$$\binom{6}{2} \cdot 0.05^2 = \frac{6!}{2!4!} \cdot 0.0025 = \frac{6 \cdot 5 \cdot 4!}{2 \cdot 1 \cdot 4!} \cdot 0.0025 = 15 \cdot \frac{1}{400} = \frac{3}{80}$$
it means the number of combinations possible when you pick 2 items out of n, that is n(n-1)/(2*1)
