Mathematics

You're counting the number of ways to choose 3 distinct positions from $n+1$ items, then multiplying by 2. The key insight is recognizing that $\sum_{0 \le i < j < k \le n} 1$ gives you $\binom{n+1}{3}$—the number of such triples—so multiplying by 2 is just scaling that count. Think of it as: how many ordered triples satisfy the constraint, and what does that formula look like?

You're counting the number of ways to choose 3 distinct positions from $n+1$ items, then multiplying by 2. The key insight is recognizing that $\sum_{0 \le i < j < k \le n} 1$ gives you $\binom{n+1}{3}$—the number of such triples—so multiplying by 2 is just scaling that count. Think of it as: how many ordered triples satisfy the constraint, and what does that formula look like?