You flip each coin. How many outcemes are possible?

To determine the number of possible outcomes when flipping multiple coins, you can use the following approach: ### **General Formula** If you have **_n_** coins, each coin has **2** possible outcomes: **Heads (H)** or **Tails (T)**. Since each coin flip is independent of the others, the total number of possible outcomes is calculated by multiplying the number of outcomes for each coin together. **Total Outcomes = 2 × 2 × 2 × ... × 2 (n times) = 2ⁿ** ### **Examples** 1. **Flipping 1 Coin:** - **Outcomes:** H, T - **Total Outcomes:** 2¹ = 2 2. **Flipping 2 Coins:** - **Outcomes:** HH, HT, TH, TT - **Total Outcomes:** 2² = 4 3. **Flipping 3 Coins:** - **Outcomes:** HHH, HHT, HTH, THH, HTT, THT, TTH, TTT - **Total Outcomes:** 2³ = 8 ### **Why 2ⁿ?** Each coin represents a binary choice (H or T). For every additional coin you add, the number of possible combinations doubles. This exponential growth is why the formula uses 2 raised to the power of the number of coins. ### **Conclusion** - **If you have _n_ coins, the number of possible outcomes when flipping all of them is 2ⁿ.** **Feel free to specify the number of coins you're considering if you need a more tailored answer!**