Permutation word problem

Question

A box has 7 green items and 5 black items. We randomly pick 2 items from the box. What are the odds that both items are green if we know that the first item is green?

Answer 1

The probability that both of the picked items are green is $\frac{\binom{6}{1}}{\binom{11}{1}}$. This is because we have already picked one green item by the given condition, thus giving us 6 green items and 11 items remaining in total;out of which we have to pick only one green ball in order for the condition to be satisfied. Thus, the odds in favour of both items being green provided one item picked is already green is 6 to 11.