Evaluating binomial coefficients $$\binom{1}{0},\binom{1}{1},\binom{1}{2}$$
 What does this mean, and how do I achieve an numerical value when trying to solve a proof or problem in this form?
As you know, in general, $\binom{n}{k}$  is a number with value = the count of ways $k$ objects can be selected out of $n$ objects (when we are not interested in the order of selection, but just in the set of elements that are chosen).

Respectively:


$\binom{1}{0} = 1$ since there is only one way to select 0 elements out of 1 - just do not select anything. 
$\binom{1}{1} = 1$ too, since we must just select the only element we have. We know also that $\binom{1}{1} = \binom{1}{0}$, because $1=1-0$.
$\binom{1}{2} = 0$ since we cannot select 2 elements out of 1, at all. In general, $\binom{n}{k} = 0$, if $k&gt;n$ or $k&lt;0$.
An expression for ${n}\choose{k}$ that you can use to compute it is $\frac{n}{k!(n-k)!}$.

The actual interpretation of the values is:


$\binom{1}{0} = 1$ means there is only one way to select 0 elements out of 1element
$\binom{1}{1} = 1$ means we one element and select the only element we have.
$\binom{1}{2} = 0$ means we cannot select 2 elements out of 1 so 0