SOLUTION: A bookcase contains 6 different math books and 12 different physics books. If a student randomly selects two of these books, then what is the probability he or she selects two book

There are 2 ways to do this problem.  Take your pick:

First way:
1. Calculate the number of ways to select ANY two books. 
   18 choose 2 = 18C2 = 153.
2. Subtract the number of ways to select a math book and a physics book.
   Choose the math book 6 ways and the physics book 12 ways, that's 6*12=72
3. No. of ways: 153-72 = 81 ways.
Probability 81/153 = 9/17


Second way:
Case 1: Select two math books "6 choose 2" = 6C2 = 15 ways.
Case 2: Select two physics books "12 choose 2" = 12C2 = 66 ways.
Total: 15+66 = 81 ways. 
Calculate the number of ways to select ANY two books. 18C2 = 153
Probability: 81/153 = 9/17

Edwin