What's the probability of picking out 5 white and 3 red balls from a bag containing 12 white and 3 red balls? That is all the red balls and 5 white from the bag leaving 7 white balls.

Answer 1

Just consider each ball's chances as it is drawn:

3/15 * 2/14 * 1/13 * 12/12 * 11/11 * ... = 1/455

Note that after all the red balls are drawn, there is a 100% chance that the rest will be white.

Also, the order does not matter. If the order were WWRWWRWR the chances would be

12/15 * 11/14 * 3/13 * 10/12 * 9/11 * 2/10 * 8/9 * 1/8 = 1/455