what is the probability that both red and blue marbles were removed from the bag?

Question

There are 3 red and 4 blue marbles in a bag. Simultaneously at random, 3 marbles are removed from the bag. If at least 2 of the marbles removed from the bag are blue, then what is the probability that both red and blue marbles were removed from the bag?

Answer 1

n(2 blue and 1 red) = C(4,2)C(3,1) = 6*3 = 18

n(3 blue) = C(4,3)C(3,0) = 4

P(blue and red | at least 2 blue) = P(2 blue | at least 2 blue) =18/(18+4) = 9/11 = .8182