Consider a drawer with $6$ pens: $2$ blue, $2$ red, $1$ yellow and $1$ green. We choose two pens without replacement. What is the probability of extracting one blue pen second?
Answer given: $21/50$
I've tried many different methods, including finding the probability of picking a blue pen then a blue pen and then multiplying it by the probability of picking a blue pen first. Then adding that to the probability of picking a non-blue pen then a blue pen, then multiplying it by the probability of picking up a non-blue pen first. That method gives me $1/3$, and all other methods give me answers don't get close to the answer given.
Any help would be greatly appreciated!