Probability of a Two Boxes Having The Same Number of Distinct Balls

Given an array ballCount representing the number of balls of each color, randomly divide all balls into two boxes with equal total balls. Return the probability that both boxes have the same number of distinct colors.

Examples
Input: [1,1]
Output: 1
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Probability of a Two Boxes Having The Same Number of Distinct Balls

Given an array ballCount representing the number of balls of each color, randomly divide all balls into two boxes with equal total balls. Return the probability that both boxes have the same number of distinct colors.