TITLE: What is the probability that white balls will be in the same box?
QUESTION [6 upvotes]: I have trouble computing a probability, I wish someone can help me with this. This is not a homework or anything like that.
So there are $71$ balls, and two of them are white, the rest are black.
The balls are randomly distributed between $14$ boxes. $5$ balls in each box, one box will have $6$ balls. What is the probability that white balls will be in the same box?

REPLY [4 votes]: I saw this as the set of pairs-in-the-same-box vs all pairs:
$a = (5\mathbb{C}2).13 + 6\mathbb{C}2 = 145\ \text{pairs} \\
b = 71\mathbb{C}2 = 2485\ \text{pairs} \\
\frac{a}{b} = \frac{145}{2485} \approx 5.8\%$
Where $a$ is the collected set of co-located pairs from each of the boxes (summed because they are independent), and $b$ is all the pairs of balls in total.