# Conditional probability and combinatorics - Picking balls, again

You have 2 boxes that contains 100 balls each, and the balls can be white, blue, red, or half red and blue.

Box A contains:

• 90 white balls
• 10 red balls

Box B contains:

• 86 white balls
• 4 red balls
• 9 blue balls
• 1 red and blue ball

If you don't know which box you pick a ball from (the probability is equal for what box you chose), what is the probability for pulling exactly 2 white balls and 1 red ball, if you don't put it back and don't take a look at the balls until all 3 are pulled from the box you chose? (You only pick 3 balls).

I thought this would be pretty straight forward by using combinatorics: