Answer to Question #239403 in Combinatorics | Number Theory for sam

Question

True or false:

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

Answer 1

Solution:

We know that  $\displaystyle{{n}\choose{r}}=\dfrac{n!}{r!(n-r)!}$ , where $n\ge r;n,r\ge 0$

But in  $\displaystyle{{2}\choose{10}}$, $n=2,r=10$  which is against the definition of binomial coefficient.

Thus, the value of  $\displaystyle{{2}\choose{10}}$ does not exist, neither it is zero.

Hence, given statement is false.