Let $n\ge 2$ and $d\ge 1$ be integers with $d\mid n$, and let $x_1,x_2,\ldots x_n$ be real numbers such that $x_1+x_2+\cdots + x_n=0$. Show that there are at least $\binom{n-1}{d-1}$ choices of $d$ indices $1\le i_1<i_2<\cdots <i_d\le n $ such that $x_{i_{1}}+x_{i_{2}}+\cdots +x_{i_{d}}\ge 0$.