Evaluate the expression 4! • 3! 12 30 144 5,040
The Correct Answer and Explanation is:
✅ Correct Answer: 5,040
Step-by-step Evaluation:
We are asked to evaluate this expression:
4! • 3! 12 30 144 5,040
To properly evaluate it, we first need to clarify what part of this is the actual expression and what are just numbers listed afterward (possibly as distractors or reference points).
The actual mathematical expression is likely just:
4! • 3!
Let’s break this down:
Factorial Review:
- n! (read as “n factorial”) is the product of all positive integers from 1 to n. So,
- 4! = 4 × 3 × 2 × 1 = 24
- 3! = 3 × 2 × 1 = 6
Now multiply the two:
- 4! • 3! = 24 × 6 = 144
So, the result of 4! • 3! is 144.
Now what about the rest?
You wrote:
4! • 3! 12 30 144 5,040
This looks like a list of possible answer choices — common in multiple-choice questions.
So among:
- 12
- 30
- 144
- 5,040
The correct value from evaluating 4! • 3! is 144 ✅
Why You Might See 5,040:
- 7! = 5,040, which might be listed to confuse you, especially if someone mistakenly adds 4 + 3 = 7 and computes 7!.
But that’s incorrect because 4! • 3! ≠ 7!
Final Answer: 144
Explanation:
To evaluate the expression 4! • 3!, we must understand what factorials mean. The factorial of a number n, written as n!, is the product of all positive integers from 1 to n. For example, 4! means 4 × 3 × 2 × 1, which equals 24. Similarly, 3! is 3 × 2 × 1 = 6.
The expression is 4! • 3!, which means we multiply the two results:
4! • 3! = 24 × 6 = 144.
After evaluating, we notice a series of numbers: 12, 30, 144, 5,040. These are likely multiple-choice options designed to distract or test your understanding of factorials. For instance, 5,040 is 7!, which a student might incorrectly choose if they added 4 + 3 and took the factorial of that sum. However, this is not the correct interpretation.
Sometimes, students confuse n! + m! or (n + m)! with n! • m!, but each expression has a different meaning. n! • m! is the product of the factorials of two separate numbers, not the factorial of their sum.
The key to solving factorial problems is to evaluate each factorial independently, then follow the standard order of operations. In this case, multiply the two results after calculating them.
Thus, the correct evaluation of 4! • 3! is 144, making 144 the correct answer.
