A coin is tossed three times and the outcomes are recorded. How many possible outcomes are three ?
How many possible outcomes if the coin is tossed : Four times , Five times , n times ?

Answer

To solve the problem of how many possible outcomes there are when a coin is tossed multiple times, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Outcomes of a Single Coin Toss:**
- When a coin is tossed once, there are 2 possible outcomes: Heads (H) or Tails (T).

2. **Calculating Outcomes for Multiple Tosses:**
- If the coin is tossed multiple times, each toss is independent of the others. Therefore, the total number of outcomes can be calculated by multiplying the number of outcomes for each toss.
- For example, if the coin is tossed 3 times, the outcomes can be represented as:
- First toss: 2 outcomes (H or T)
- Second toss: 2 outcomes (H or T)
- Third toss: 2 outcomes (H or T)

3. **Using Exponents to Simplify the Calculation:**
- Since each toss has 2 outcomes, and there are 3 tosses, the total number of outcomes is:
\[ \text{Total Outcomes} = 2 \times 2 \times 2 = 2^3 = 8 \]

4. **Generalizing the Formula for n Tosses:**
- If the coin is tossed \( n \) times, the total number of outcomes can be generalized as:
\[ \text{Total Outcomes} = 2^n \]
- This means:
- For 4 tosses: \( 2^4 = 16 \)
- For 5 tosses: \( 2^5 = 32 \)
- For \( n \) tosses: \( 2^n \)

### Final Answers:
- The number of possible outcomes when a coin is tossed 3 times is **8**.
- The number of possible outcomes when a coin is tossed 4 times is **16**.
- The number of possible outcomes when a coin is tossed 5 times is **32**.
- The number of possible outcomes when a coin is tossed \( n \) times is **\( 2^n \)**.