Probability notation two numbers stacked inside brackets I have a very simple question. Could someone elaborate on the notation of two numbers stacked inside brackets? Such as:
$$
        \begin{pmatrix}
        5 \\
        1 \\
        \end{pmatrix}
$$

Assume $m\geq n$ are nonnegative integers. We define $\binom{m}{n}$ as 
$$ 
\binom{m}{n} := \frac{m!}{n!\,(m-n)!} = \dfrac{m(m-1)(m-2)\cdots 3\cdot 2\cdot 1}{(n(n-1)\cdots 3\cdot 2\cdot 1)((m-n)(m-n-1)\cdots 3\cdot 2\cdot 1)},  
$$ 
and read $\binom{m}{n}$ as "$m$ choose $n$". As others have mentioned above, this is called the $\textbf{binomial coefficient}$. 
Let's go back to the example $\binom{5}{1}$. One could think of this as the number of ways to choose $1$ object in a bag of $5$ objects. If you have a bag with $5$ objects, how many ways are there to pick one item? There are $5$ ways. 
That is, 
$$
\binom{5}{1}=\frac{5!}{1! (5-1)!} = \frac{5\cdot 4\cdot 3\cdot 2\cdot 1}{1\cdot 4\cdot 3\cdot 2\cdot 1} = 5.
$$
Now consider the example $\binom{5}{2}$. How many ways are there to pick two items in a bag with $5$ items (without replacement)? 
There are $5$ ways to pick the first item (let's call this item $A$) and then there are $4$ ways to pick the second item (let's call this item $B$). Since the ordering does not matter, we divide $5\cdot 4$ by $2$ to obtain: 
$$
\frac{5\cdot 4}{2} = 10,  
$$ 
which is 
$$
\binom{5}{2} = \frac{5!}{2!\, 3!} = \frac{5\cdot 4\cdot 3\cdot 2\cdot 1}{2\cdot 1\cdot 3\cdot 2\cdot 1} = 10.  
$$
