How to simplify the sum $\sum_{k=0}^{n}\binom n k q^k(1-p-q)^{n-k}$?

Question

I am trying to simplify the following sum: $$\sum_{k=0}^{n}\binom n k q^k(1-p-q)^{n-k}.$$ There are no specifications on $p$ and $q$.

Answer 1

By the Binonmial Theorem, $$\sum_{k=0}^{n}\binom n k q^k(1-p-q)^{n-k} =(q+(1-p-q))^n=(1-p)^n.$$