Problem Solving

Hello,

Can you please tell me if my solution is correct here?

Three balls are picked at random, without replacement, from a bag that contains 4 red and 5 blue balls, what is the probability of picking exactly one red ball?

(This is from GMAT Word Problems book. The answer given there seems to be wrong.)


P(RBB) = (4/9)(5/8)(4/7) = 10/63

Total number of ways to draw one red and two blue balls = (3 x 2 x 1)/( 2! ) = 3

Hence, total number of ways to pick exactly one red ball = (10/63)(3) = 10/21

Is this correct?


Thanks a lot,
Sri