Let's analyze and solve problem 5(b) based on the content extracted from the image.

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### Problem 5(b) Description:

The problem seems to be asking:

**Given that a player has 5 coins, each of which can show either heads (H) or tails (T), what is the probability that exactly 3 of these coins show heads?**

### Solution:

1. **Determine the total number of possible outcomes:**

   - Since each coin can show either heads or tails, and there are 5 coins, the total number of possible outcomes is:
     \[
     2^5 = 32
     \]

2. **Calculate the number of favorable outcomes:**

   - We need exactly 3 heads. The number of ways to choose 3 heads out of 5 coins is given by the combination formula:
     \[
     \text{Number of favorable outcomes} = \binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{5 \times 4}{2 \times 1} = 10
     \]

3. **Calculate the probability:**

   - The probability of getting exactly 3 heads is the ratio of the number of favorable outcomes to the total number of outcomes:
     \[
     \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{10}{32} = \frac{5}{16}
     \]

### Final Answer:

The probability that exactly 3 out of the 5 coins show heads is \(\frac{5}{16}\).

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Would you like more details or have any questions on this problem? Here are some related questions that you might find helpful:

1. How do you calculate combinations like \(\binom{5}{3}\)?
2. What is the formula for calculating the total number of outcomes in a probability scenario?
3. How does the concept of independent events apply to this problem?
4. What would be the probability if we needed exactly 2 heads instead of 3?
5. Can you explain the binomial distribution and how it relates to this problem?
6. What would happen to the probability if there were 6 coins instead of 5?
7. How can we verify the answer using a different method, such as listing all possible outcomes?
8. What if we wanted to find the probability of getting at least 3 heads?

**Tip:** When dealing with probabilities, always ensure that the total number of outcomes is correctly calculated, as any mistake there can lead to incorrect results.

Learn how to calculate the probability of getting exactly 3 heads out of 5 coins. This problem involves combinatorics and probability theory, focusing on the binomial coefficient formula. Suitable for high school students.

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