Question

True or False:

The value of the binomial coefficient $\displaystyle{{2}\choose{10}}$ is zero

Answer 1

The binomial coefficient for non negative integers is given by:

$\begin{pmatrix} n \\ k \end{pmatrix}=\begin{cases} \frac{n!}{k!(n-k)!}\quad \text{for} ~0 \leq k <n \\ 0 \quad \quad \quad \quad\text{otherwise}\end{cases}$

Note that from the given binomial coefficient that $n=2$ and $k=10$

Since $k$ is not less than $n$ ; therefore the value of the given binomial coefficient is equal to zero.

The given statement is true.