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

 5x + 10y ≥ 60 ⇒ x+2y ≥ 12           (i)  

                x + y ≤ 12                                     (ii)  

Step-by-step explanation:

    Let the hours spent on exercising horse be x

    Let the hours spent on cleaning stalls be y

According to question:

Rob can't work more than 12 hours. So eq. (i) will be x + y ≤ 12

Rob earns $5 an hour by exercising horses and $10 an hour cleaning stalls and he must make $60 . So eq. (ii) will be 5x + 10y ≥ 60.

Dividing eq. (ii) by 5, it will become x + 2y ≥ 12.

∴ system of inequalities are x + y ≤ 12 and x + 2y ≥ 12.