1. ## Combinations/Probability

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.

2. 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.

3. Originally Posted by Fel
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.
$D_k=\dbinom{15}{k}\dbinom{10}{6-k}$.

Consider $\dfrac{{\sum\limits_{k = 3}^6 {D_k } }}
{\binom{25}{6}}$