Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 58 bank accounts, we want to take a random sample of four accounts in order to learn about the population. How many different random samples of four accounts are possible?

To determine how many different random samples of four bank accounts are possible from a population of 58, we use the concept of combinations. In combinations, the order of selection does not matter, so we use the combination formula:

\[
\binom{N}{n} = \frac{N!}{n!(N - n)!}
\]

Where:
- \( N = 58 \) is the population size,
- \( n = 4 \) is the sample size,
- \( N! \) denotes the factorial of \( N \).

Substitute the values:

\[
\binom{58}{4} = \frac{58!}{4!(58 - 4)!} = \frac{58!}{4!54!}
\]

We can simplify this calculation by canceling out the common terms from \( 58! \) and \( 54! \), and only compute the remaining part:

\[
\binom{58}{4} = \frac{58 \times 57 \times 56 \times 55}{4 \times 3 \times 2 \times 1}
\]

Now, let's calculate this.

\[
58 \times 57 = 3306, \quad 3306 \times 56 = 185136, \quad 185136 \times 55 = 10182480
\]

\[
4 \times 3 \times 2 \times 1 = 24
\]

Now divide:

\[
\frac{10182480}{24} = 424270
\]

Thus, the number of different random samples of four accounts is \( \boxed{424270} \).

Would you like more details or have any other questions?

Here are five related questions you may want to consider:
1. How does simple random sampling differ from stratified random sampling?
2. What are the assumptions of simple random sampling?
3. How can we ensure randomness when selecting a sample?
4. What are the possible biases in simple random sampling?
5. How can increasing the sample size improve the reliability of inferences?

**Tip:** When calculating combinations, cancel out common factorials to simplify the process and avoid large computations.

Find out how many random samples of four accounts can be drawn from a population of 58 bank accounts. Learn how to apply the combination formula to solve this simple random sampling problem. Suitable for high school students in Grades 10-12.

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