195930

When I first looked at this problem, I started writing down combinations to button it up (starting from the first button). 1234,1243,1324... In total, I have 6 combinations. Starting from the second button, I already know that there will be 6 combinations because I did the first one. That works with the third and fourth too. I know that there are 4 buttons so all I need to do now is multiply 6 by 4, which is 24. In total, there are 24 ways to button up that coat

. If it was 5 buttons I would simply multiply every whole number from 5 and below to get the answer. 5 x 4 x 3 x 2 x 1 = 120. For 6 I would just do the same thing but starting from 6 and below - 6 x 5 x 4 x 3 x 2 x 1 = 720. That's how I got my solutions.