1.1.4 problem 4

(a)

There are $\left(\frac{n}{2}\right)$ matches.

For a given match, there are two outcomes. Each match has two possible outcomes. We can use the multiplication rule to count the total possible outcomes.

$$2^{\left(\frac{n}{2}\right)}$$

(b)

Since every player plays every other player exactly once, the number of games is the number of ways to pair up $n$ people.

$$\left(\frac{n}{2}\right)$$