Football Match Outcomes
1. The problem asks to calculate the total number of possible outcomes for 20 football matches, where each match can result in one of three outcomes: win, lose, or draw.
2. Since each match has 3 possible outcomes, and there are 20 matches, the total number of combined outcomes is calculated by raising 3 to the power of 20.
3. Mathematically, this is expressed as:
$$3^{20}$$
4. Calculating the value:
$$3^{20} = 3 \times 3 \times \cdots \times 3 \text{ (20 times)} = 3,486,784,401$$
5. Therefore, the total number of possible outcomes for all 20 matches combined is 3,486,784,401.
This means there are over three billion different ways the results of these 20 matches can occur when considering win, lose, or draw for each match.