There are 16 teams in a football league. Two teams are going to be chosen at random to play a match. Work out the number of differen matches that could take place.

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To determine the number of different matches that can take place in a league of 16 teams, we need to calculate how many unique pairs of teams can be formed. Here's how you can work it out:

1. **Understanding the Problem:**
   - **Total Teams:** 16
   - **Teams per Match:** 2
   - **Order Doesn't Matter:** A match between Team A and Team B is the same as a match between Team B and Team A.

2. **Using Combinations:**
   Since the order in which the teams are selected doesn't matter, we use combinations (not permutations).

The formula for combinations is:
   $$
   C(n, k) = \frac{n!}{k!(n - k)!}
   $$
   Where:
   - $$ n $$ = total number of items (teams) = 16
   - $$ k $$ = number of items to choose = 2

3. **Calculating the Number of Matches:**
   $$
   C(16, 2) = \frac{16!}{2!(16 - 2)!} = \frac{16 \times 15}{2 \times 1} = \frac{240}{2} = 120
   $$

4. **Alternative Method (Step-by-Step Selection):**
   - **First Team:** 16 choices
   - **Second Team:** 15 choices
   - **Since order doesn't matter, divide by 2 to avoid double-counting:**
     $$
     \frac{16 \times 15}{2} = 120
     $$

**Therefore, there are 120 different possible matches that could take place.**

**Answer:** 120
There are 120 different possible matches that could take place.

There are 16 teams in a football league. Two teams are going to be chosen at random to play a match. Work out the number of differen matches that could take place.

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