Probability Question... Plz help?

Question

A bag contains 9 red balls, 10 yellow balls and 5 blue balls. Two balls are drawn at random from the bag without replacement. What is the probability that they are of different colors??....

Answer 1

There are 3 combinations, and associated probabilities:

RY = 9/24 x 10/23 = 90/552

RB = 9/24 x 5/23 = 45/552

BY = 5/24 * 10/23 =  50/552

Since they are independent, the probability of any of them happening is just the sum of their individual probabilities:

(90+45+50)/552 = 185/552 = 0.335

Answer 2

Red balls: 9 out of 24: 37.5%

Yellow balls: 10 out of 24: 41.66666%

Blue balls: 5 out of 24: 20.83%

Answer 3

answer

= [9*(24-9) + 10*(24-10) + 5*(24-5)] / 24*23

= [9*15 + 10*14 + 5*19] / 24*23

= 370 / 552

= 185 / 276

= 0.67029