General Approaches to counting problems Throughout the my discrete mathematics course I have continually encountered difficulties with counting style problems. Whether they are counting members of a partition or counting the number of ways something can be done with ordering, without ordering, with multiple groupings etc. I feel as though I am missing out on a more fundamental idea because as I venture away from simple factorial and r choose k problems I begin to get lost. Has anyone else had this experience and if so what helped you resolve your issues. 
 A: As a teaching assistant in an undergraduate combinatorics course, I'm often asked this exact question. To be honest this is a hard one since it is a highly non-specific question. 
But, some general tips can be:


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*A lot of exercises and problems are simple-straightforward counting problem with a twist. For example - How many binary string of length 10 are they (so far really trivial) that don't have 3 consecutive 1s (the twist). I advise you to first do a sanity check and see that you can solve the question if you ignore the extra restriction. After that add it back and try to see what does it changes. This can be helpful in figuring "what's going on" and may help to cope with the initial "shock" students often have when solving exercises.

*Try playing with small and simple cases. Pick some small instances of the problem. Say, if the question deals with n people pick n=4, or even if the question asks about strings of length 1000 reduce it to 5. This way you can start "feeling" what you are asked about and how you might approach it.

*Practics, practice, practice. The more exercises you solve the better you will understand the patterns and the usefulness of each mathematical definition.
Good luck!
