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Discrete Mathematics

# Combinations: Level 2 Challenges

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 the castle was 4 blocks north and 5 blocks east. If I were to travel only north and east, how many routes did I have to get to the castle?

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?

12 students were present at a board meeting. Each student shook hands with all of the other students before & after the meeting. How many hand shakes were there?

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