Count Even-Product Triplets
Given a list of integers, count how many unordered triplets $(a, b, c)$ -- chosen from distinct positions in the list -- have an even product.
**Constraints:**
-
\leq n \leq 10^5$ where $n$ is the length of the list
- Elements may be positive, negative, or zero
- Triplets are unordered combinations (not permutations)
**Examples:**
Example 1: `nums = [1, 2, 3, 4, 5]`
Output: `9`
Explanation: Total triplets = $\binom{5}{3} = 10$. The only odd triplet is $\{1, 3, 5\}$. So
0 - 1 = 9$.
Example 2: `nums = [1, 3, 5, 7]`
Output: `0`
Explanation: All elements are odd, so every product is odd. $\binom{4}{3} - \binom{4}{3} = 0$.
Example 3: `nums = [2, 4, 6]`
Output: `1`
Explanation: Only one triplet exists and it contains all even numbers, so product is even.
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