Teresa and julia are among 10 students who have applied for a trip to washington, d. c. two students from the group will be selected at random for the trip. what is the probability that teresa and julia will be the 2 students selected?

With 10 students you have 10 choices for the first student to go, then 9 choices for the second student to go. That would seem to be 90 ways to choose the people to go on the trip. But the order doesn't matter. You don't care if Alice is chosen, then Bob, or vice versa. So divide this number by 2 to account for the double-counting. 

There are 45 ways to pick the 2 people out of 10. 
C(10,2) = (10 x 9) / (2 x 1) = 45 ways 

Selecting Teresa and Julia is just one of those possible outcomes, so the probability is: 
1/45