1. The problem statement, all variables and given/known data There is a large\infinite amount of balls in a basket to pick from. Each ball in the basket is with the same probability (33.33...%) either black, white or gray. No other colors exist. You first pick 4 balls out of the basket. Then you pick 2 more balls out of the basket. Question: What is the probability that the last 2 picked balls are fully 'contained' in the 4 balls? Notes: BOTH balls have to be of a same color of one of balls in the 4, and they both have to be unique. Thus: One black ball in the 4 counts only for one black ball in the last 2, etc... 2. Relevant equations Simpler case: only one ball is drawn after the first four. Then the probability is: -- P(1 ball is contained in the 4) =[itex]1 - 2/3*2/3*2/3*2/3 = 1-(2/3)^4[/itex] == CORRECT The analytical solution for the full original 4+2 balls case is: [itex]399/729[/itex]. I have written and tested a computer program to find all the solutions for this, so it should be correct. 3. The attempt at a solution -- P(1 ball is contained in the 4) AND P(1 ball is contained in the 4) =[itex](1-(2/3)^4) ^2[/itex] == WRONG I have no idea how to continue from here or why this is wrong.