Studying for a final:
1) Suppose we have four indistinguishable red balls, 6 indistinguishable blue balls, and 2 indistinguishable green balls. How many different color patterns can be obtained by arranging these balls in a straight line?
I did ${12\choose4} {12\choose6} {12\choose2} = 30,187,080$ but that's definitely not correct.
2) A fair, ordinary six-sided die is colored red on one face, blue on two faces, and green on the remaining three faces. Find an explicit expression (but do not simplify it) for the probability that, in the 12 rolls fo this die, red will come up 4 times, blue will come up 6 times, and green will come up 2 times? Hint: What is the probability of observing the sequence RBBRGBBRGBRB?
I'm not really sure what to do and the hint only made me even more confused.