196191

If you have 3 buttons, then there would be 18 ways to button up the jacket. If you have 4 buttons, then there would be 24 combinations, 5 buttons would be 30 combinations, and 6 buttons would have 36 combinations. I think this because if you have 4 buttons, for example, then there are 6 ways you can button it, starting with the top one. Because there are 4 buttons, you times 6x4 and get 24. I then used this method to work out the other answers.