very interesting problem!!!

Hello all, I hope some of you can help me with this problem...

There are 30 total components in the bag. 21 are good and 9 are bad. It takes 6 components to buid one assembly (we can build 5 total assemblies), and components will be pulled randomly out of bag. What is probability for each assembly to have all 6 good components, and therefore be a good assembly (good assebmly has to have all 6 good components).

I tried using (0.7)^6 formula, but that formula accounts for any 6 good components in a row, which is not correct. If we pulled 6 good components in a row, but ther are pulled 3rd to 9th we will

not have a good assembly. Having a good assembly will require pulling good components from 1 to 6, or 7 to 12 and so on.

I tried formula mentioned above, where there is 70% chance to pull a good component out of bag, but this formula works only for infinite sample where cases are indenpendent from eachother. In our case we have 30 components total.

Thanks