1. Consider a graph with $5$ points, where every point is connected by a line to every other point. (A graph like that is sometimes called a complete graph with 5 points, or $K_5$)
   1. How many lines are there within this graph?
   2. How many triangles (groups of 3 points, all of ...

1. Is the formula $(x+5)^2 = x^2 + 25$ always true? If it is, find a way to prove that it is true. If it is not, provide a counterexample (a value of $x$ which shows that the formula is not always true).
2. Write down all the subsets of the ...

If there are 8 people at a party,

1. How many possible ways are there for all of them to line up (to get drinks, for example)?
2. How many possible ways are there to pick four of those people out of the drink line, keeping them in order?
3. How many ways ...