Compute The Following: 5 ! 5! 5 ! A. 60 B. 120 C. 15 D. 5
Introduction
In mathematics, a factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. In other words, it is the result of multiplying all whole numbers from n down to 1. For instance, the factorial of 5 (denoted as 5!) is equal to 5 × 4 × 3 × 2 × 1. In this article, we will explore the concept of factorials and compute the value of 5!.
What is a Factorial?
A factorial is a mathematical operation that involves multiplying a series of descending numbers. The factorial of a number n (denoted as n!) is calculated by multiplying all positive integers from n down to 1. For example, the factorial of 5 (5!) is calculated as follows:
5! = 5 × 4 × 3 × 2 × 1
Computing 5!
Now that we have a clear understanding of what a factorial is, let's compute the value of 5!. We will follow the order of operations and multiply the numbers in the correct order.
5! = 5 × 4 × 3 × 2 × 1 = 5 × 4 × 3 × 2 = 5 × 4 × 6 = 5 × 24 = 120
Therefore, the value of 5! is 120.
Comparing the Options
Now that we have computed the value of 5!, let's compare it with the given options.
A. 60 B. 120 C. 15 D. 5
As we can see, the correct answer is option B, which is 120.
Conclusion
In this article, we explored the concept of factorials and computed the value of 5!. We learned that a factorial is a mathematical operation that involves multiplying a series of descending numbers. We also compared the computed value of 5! with the given options and found that the correct answer is option B, which is 120.
Frequently Asked Questions
Q: What is a factorial?
A: A factorial is a mathematical operation that involves multiplying a series of descending numbers.
Q: How is the factorial of a number calculated?
A: The factorial of a number n (denoted as n!) is calculated by multiplying all positive integers from n down to 1.
Q: What is the value of 5!?
A: The value of 5! is 120.
Q: Which option is correct?
A: The correct answer is option B, which is 120.
Additional Resources
For more information on factorials and other mathematical concepts, please refer to the following resources:
References
- Weisstein, Eric W. "Factorial." From MathWorld--A Wolfram Web Resource.
- Khan Academy. "Factorials."
Understanding Factorials and Computing 5! =====================================================
Q&A: Factorials and 5!
Q: What is a factorial?
A: A factorial is a mathematical operation that involves multiplying a series of descending numbers. It is denoted by an exclamation mark (!) and is calculated by multiplying all positive integers from the given number down to 1.
Q: How is the factorial of a number calculated?
A: The factorial of a number n (denoted as n!) is calculated by multiplying all positive integers from n down to 1. For example, the factorial of 5 (5!) is calculated as follows:
5! = 5 × 4 × 3 × 2 × 1
Q: What is the value of 5!?
A: The value of 5! is 120. This is calculated by multiplying all positive integers from 5 down to 1:
5! = 5 × 4 × 3 × 2 × 1 = 120
Q: Which option is correct for the value of 5!?
A: The correct answer is option B, which is 120.
Q: What is the difference between a factorial and a product?
A: A factorial is a specific type of product that involves multiplying a series of descending numbers. A product, on the other hand, is a general term that refers to the result of multiplying two or more numbers together.
Q: Can you give an example of a factorial that is not 5!?
A: Yes, a simple example is 4!. The factorial of 4 (4!) is calculated as follows:
4! = 4 × 3 × 2 × 1 = 24
Q: How do you calculate the factorial of a negative number?
A: The factorial of a negative number is not defined in mathematics. Factorials are only defined for non-negative integers.
Q: What is the relationship between factorials and permutations?
A: Factorials are closely related to permutations. The number of permutations of n objects is equal to n!. This means that if you have n objects and you want to arrange them in a specific order, there are n! possible ways to do so.
Q: Can you give an example of how factorials are used in real-life situations?
A: Yes, factorials are used in many real-life situations, such as:
- Calculating the number of possible outcomes in a game or experiment
- Determining the number of ways to arrange objects in a specific order
- Calculating the probability of certain events occurring
Q: How do you calculate the factorial of a large number?
A: Calculating the factorial of a large number can be challenging, but there are several methods that can be used, such as:
- Using a calculator or computer program
- Using a formula or algorithm to calculate the factorial
- Breaking down the factorial into smaller parts and calculating each part separately
Q: What is the significance of factorials in mathematics?
A: Factorials are an important concept in mathematics, as they are used to calculate the number of permutations and combinations of objects. They are also used in many real-life situations, such as calculating probabilities and determining the number of possible outcomes in a game or experiment.
Additional Resources
For more information on factorials and other mathematical concepts, please refer to the following resources: