I'm trying to brush up a bit on basic combinatiorics and I'm finding that unfortunately I'm quite bad at it. I tried solving the following exercises without real success:
How many ways are there to arrange in a row 6 red balls, 6 yellow balls and 2 blue balls such that:
- The rightmost ball is red and there are no adjacent red balls.
- The rightmost ball is yellow and there are no adjacent red balls.
- There are no adjacent red balls and no adjacent blue balls
All my attempts were overly complicated and relied too much on brute force. I would really appreciate it if someone could show me how to elegantly approach such a question.
Note: I added the homework tag in hope it would get the question further exposure but this is not actually a homework task so if possible I'd prefer to see a complete solution rather than hints.
Thanks in advance!!