Maybe
A = 10 choose i
B = 15 choose 6-i
C = 25 choose i
P(D_i) = AB / C
What could be done is checking that the sum of D_i is one.
A rental car service facility has 10 foreign cars and 15 domestic cars. Choose 6 cars at random. Let D_i={exactly i of 6 cars chosen are domestic}, i=0,1,2,...6. What is the probability of at least 3 cars out of the 6 being domestic? I'm not sure how to solve this. Any help is appreciated.