Question 24
For positive integers $x_{1}, x_{2}, \ldots, x_{n}$ satisfying $x_{1}+\cdots+x_{n}=101 n$, prove that
$$
\binom{x_{1}}{2}+\binom{x_{2}}{2}+\cdots+\binom{x_{n}}{2} \geq 5050 n
$$
$$
\binom{x_{1}}{2}+\binom{x_{2}}{2}+\cdots+\binom{x_{n}}{2} \geq 5050 n
$$