Let's break down the given expression step by step:

$(8 \times 3) \div \left[ 15 - (2 \times 4) + 1 \right]$

1. First calculate the inner parentheses:

$2 \times 4 = 8$

So the expression becomes:

$(8 \times 3) \div \left[ 15 - 8 + 1 \right]$

2. Next, simplify the expression inside the brackets:

$15 - 8 = 7$

Then:

$7 + 1 = 8$

Now the expression is:

$(8 \times 3) \div 8$

3. Next, calculate $8 \times 3$:

$8 \times 3 = 24$

So the expression becomes:

$24 \div 8$

4. Finally, divide 24 by 8:

$24 \div 8 = 3$

So, the result is:

$\boxed{3}$

Would you like a detailed explanation of any of the steps or have any other questions?

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Related Questions:

1. How do parentheses affect the order of operations?
2. What is the difference between multiplication and division when solving expressions?
3. How would the result change if the division was performed before subtraction?
4. Can you simplify expressions with multiple operations in different orders?
5. How do you handle negative numbers in similar expressions?

Tip: Always follow the order of operations (PEMDAS) to avoid confusion when solving expressions!