Discrete Mathematics
# Combinations

How many triangles are in a fully connected pentagon with all its diagonals?

I was on vacation in England, and wanted to visit the Tower of London. The roads were laid out on a grid map, and and the castle was 4 blocks north and 5 blocks east. I also want to get at least one ice cream cone along the way. I knew that there were 2 ice cream shops that I could use, and they were conveniently located at an intersection.

If I were to travel only north and east, how many routes did I have to get to the castle?

How many ways are there to split 10 people into 2 teams so that they can play 5 on 5 basketball?