What is the probability of selecting two black tiles without replacement in simplest form?

First, note the number of tiles in each color. So there are 6 black tiles and 9 white tiles. 

The probability of picking a black tile the first time is 6/15 which is equal to 

2/5

Now, with black tile gone there are 5 black tiles and 9 white tiles.

The probability of picking a black tile now is

5/14.

But because both picks have to happen, multiply the fractions resulting in 

1/7

6(2x + 5y)6 (2x) = 12x6 (5y) = 30y12x + 30y