If (\binom{n}{0}+\binom{n}{n}=2), what type of identity does it show?

Correct answer: Boundary identity

For the boundary values of combinations, \(\binom{n}{0}=1\) and \(\binom{n}{n}=1\). Therefore, their sum is \(1+1=2\). This is a boundary identity because the number of selected objects is either 0 or all \(n\) objects. Pascal's identity instead has the form \(\binom{n}{r}=\binom{n-1}{r-1}+\binom{n-1}{r}\). Exam tip: Always remember that \(\binom{n}{0}\) and \(\binom{n}{n}\) are both 1.