1467. Probability of a Two Boxes Having The Same Number of Distinct Balls

Given 2n balls of k distinct colors. You will be given an integer array balls of size k where balls[i] is the number of balls of color i. All the balls will be shuffled uniformly at random, then we will distribute the first n balls to the first box and the remaining n balls to the other box (Please read the explanation of the second example carefully). Please note that the two boxes are consider