What is the probability that the first 2 balls are the same color while the last 2 balls are different colors? A box contains 3 Blue balls, 4 Green balls and 5 Red balls. 4 balls were picked at random without replacement. What is the probability that the first 2 balls are the same color while the last 2 balls are different colors?
What I have tried:
P(B,B,G,R) = 1/99
P(R,R,B,G) = 2/99
P(G,G,R,B) = 1/66
Therefore, the probability of (2 same color and 2 different colors) = (1/99) + (2/99) + (1/66) = 1/22 (Wrong, according to the textbook). 
Please help.

I tried $2$ different methods and got $\frac{67}{330}$ both times. The denominators of the probabilities at each draw are always $12*11*10*9=11880$ so we only have to keep track of the numerators. We also only have to draw one order of the last $2$ balls, then multiply by $2$.
$$\begin{array}{c|c}\text{Config}&\text{Ways}\\\hline
\text{BBBG}&24\\
\text{BBBR}&30\\
\text{BBGR}&120\\
\text{GGGB}&72\\
\text{GGGR}&120\\
\text{GGBR}&180\\
\text{RRRB}&180\\
\text{RRRG}&240\\
\text{RRBG}&240\\
\hline\text{Total}&2412
\end{array}$$
So I get a probability of
$$\frac{2\cdot2412}{11880}=\frac{67}{330}$$
Working out every draw also was the same:
program balls2
   implicit none
   integer i1,i2,i3,j1,j2,j3,j4
   integer total, count
   integer draw(12)
   total = 0
   count = 0
   do i1=1,10
      do i2=i1+1,11
         do i3=i2+1,12
            do j1=1,9
               if(any(j1==[i1,i2,i3])) cycle
               do j2=j1+1,10
                  if(any(j2==[i1,i2,i3])) cycle
                  do j3=j2+1,11
                     if(any(j3==[i1,i2,i3])) cycle
                     do j4=j3+1,12
                        if(any(j4==[i1,i2,i3])) cycle
                        total=total+1
                        draw = 0
                        draw([i1,i2,i3]) = 1
                        draw([j1,j2,j3,j4]) = 4
                        if(any(draw(1)+draw(2)==[1,4,5])) cycle
                        if(any(draw(3)+draw(4)==[0,2,8])) cycle
                        count = count+1
                     end do
                  end do
               end do
            end do
         end do
      end do
   end do
   write(*,*) total,count
end program balls2

Output was
   27720        5628

Which is the same ratio.
