Discrete Mathematics
# Combinations

At a party, everyone shook hands with everybody else exactly once. There were 66 handshakes. How many people were at the party?

**Details and Assumptions**:

- You can't shake your own hand.

Robbie is sitting for 9 subject papers in the GCSE O level examinations. In order to pass the examination, the number of subjects that he gets a pass grade in must be more than the number of subjects that he gets a fail grade.

The number of ways in which Robbie can pass his GCSE O level examinations is:

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. Unfortunately, there was some police activity near the hotel, and that intersection was blocked off so I could not go through it.

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