Let $\big\{X_1, X_2, ..., X_n\big\}$ be $n$ jointly exchangeable Bernoulli random variables, i.e., exchanging the order of these random variables does not change the joint distribution. If we know $$\sum_{i=1}^{n} X_i \leq m < n$$ holds for sure, does this implies that any $X_i$ and $X_j$ are negative correlated? This is quite intuitive to me because these random variables are symmetric and their sum is bounded from above...

Let $\big\{X_1, X_2, ..., X_n \big\}$ be $n$ jointly exchangeable Bernoulli random variables, i.e., exchanging the order of these random variables does not change the joint distribution. If we know that $$\sum_{i=1}^{n} X_i \leq m < n$$ holds for sure, does this imply that any $X_i$ and $X_j$ are negatively correlated? This is quite intuitive to me because these random variables are symmetric and their sum is bounded from above...