There are 15 balls named from A to O.

Question

Continuing the question: They are thrown in boxes 1, 2, 3 uniformly and at random such that each box gets 5 balls. Calculate probabilitity that A and B are in the same box.

I understand that we may need to do some form of complementary counting where the total number of outcomes are $\binom{15}{5} \times \binom{10}{5} \times \binom{5}{5}$. But I am confused over how to go ahead from this step.

Answer 1

Rare probability problem where counting is the wrong approach. Box with A has 4 empty slots out of 14. Chance is 4/14.