How to understand this double sum of probabilities

Question

Can someone please explain how this double sum works and why the LHS = RHS?

$$2 \sum_{1\leq j < k \leq N} P(F_j F_k) = \sum_{j\neq k} P(F_j F_k)$$

Answer 1

We have $$F_j \cap F_k = F_k \cap F_j,$$

Hence

$$P(F_j\cap F_k)+P(F_k \cap F_j)=2P(F_j\cap F_k)$$