A box has 9 marbles, 4 of which are white and 5 of which are red. A sample of 5 marbles is selected randomly from the box without replacement.

Question

What is the probability that exactly 3 are white and 2 are red? (Enter your answer as an exact fraction.)

Answer 1

prob(white) = 4/9
prob(red) = 5/9

prob(3 of 5 are white)
= C(5,3) (4/9)^3 (5/9)^2
= 10(64/729)(25/81)
= 16000/59049