Evaluate $5! + 2!$. A. 5,040 B. 122 C. 60

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Introduction

Factorials are a fundamental concept in mathematics, and understanding how to evaluate them is crucial for solving various mathematical problems. In this article, we will delve into the world of factorials and explore how to evaluate the expression $5! + 2!$. We will break down the problem step by step, providing a clear and concise explanation of the process.

What are Factorials?

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 example, the factorial of 5 (denoted as 5!) is equal to 5 × 4 × 3 × 2 × 1.

Evaluating $5!$

To evaluate $5!$, we need to multiply all whole numbers from 5 down to 1.

5!=5×4×3×2×15! = 5 \times 4 \times 3 \times 2 \times 1

Using the order of operations, we can simplify the expression as follows:

5!=5×(4×3×2×1)5! = 5 \times (4 \times 3 \times 2 \times 1)

5!=5×245! = 5 \times 24

5!=1205! = 120

Evaluating $2!$

To evaluate $2!$, we need to multiply all whole numbers from 2 down to 1.

2!=2×12! = 2 \times 1

2!=22! = 2

Adding $5!$ and $2!$

Now that we have evaluated both $5!$ and $2!$, we can add them together to get the final result.

5!+2!=120+25! + 2! = 120 + 2

5!+2!=1225! + 2! = 122

Conclusion

In this article, we evaluated the expression $5! + 2!$ by breaking it down into smaller parts. We first evaluated $5!$ and $2!$ separately, and then added them together to get the final result. The correct answer is $122$.

Common Mistakes to Avoid

When evaluating factorials, it's essential to remember the following:

  • Always multiply the numbers in the correct order.
  • Use the order of operations to simplify the expression.
  • Don't forget to add the results of the factorials together.

By following these tips, you can avoid common mistakes and ensure that you get the correct answer.

Real-World Applications

Factorials have numerous real-world applications, including:

  • Statistics: Factorials are used to calculate the number of permutations in a set of data.
  • Computer Science: Factorials are used in algorithms for solving problems such as the traveling salesman problem.
  • Mathematics: Factorials are used to calculate the number of ways to arrange objects in a particular order.

Final Thoughts

Evaluating factorials can seem daunting at first, but with practice and patience, you can become proficient in solving these types of problems. Remember to always follow the order of operations and use the correct notation for factorials. By mastering factorials, you can unlock a world of mathematical possibilities and apply your skills to real-world problems.

Additional Resources

For further learning, we recommend the following resources:

  • Khan Academy: Khan Academy offers a comprehensive course on factorials and permutations.
  • Mathway: Mathway is an online calculator that can help you evaluate factorials and other mathematical expressions.
  • Wolfram Alpha: Wolfram Alpha is a powerful calculator that can help you evaluate factorials and other mathematical expressions.

Q&A: Evaluating Factorials

Q: What is a factorial?

A: A factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.

Q: How do I evaluate a factorial?

A: To evaluate a factorial, you need to multiply all whole numbers from n down to 1. For example, to evaluate 5!, you would multiply 5 × 4 × 3 × 2 × 1.

Q: What is the difference between 5! and 2!?

A: 5! is the product of all whole numbers from 5 down to 1, while 2! is the product of all whole numbers from 2 down to 1.

Q: How do I add 5! and 2!?

A: To add 5! and 2!, you need to first evaluate each factorial separately and then add the results together. In this case, 5! = 120 and 2! = 2, so 5! + 2! = 120 + 2 = 122.

Q: What are some common mistakes to avoid when evaluating factorials?

A: Some common mistakes to avoid when evaluating factorials include:

  • Not multiplying the numbers in the correct order.
  • Not using the order of operations to simplify the expression.
  • Forgetting to add the results of the factorials together.

Q: What are some real-world applications of factorials?

A: Factorials have numerous real-world applications, including:

  • Statistics: Factorials are used to calculate the number of permutations in a set of data.
  • Computer Science: Factorials are used in algorithms for solving problems such as the traveling salesman problem.
  • Mathematics: Factorials are used to calculate the number of ways to arrange objects in a particular order.

Q: How can I practice evaluating factorials?

A: You can practice evaluating factorials by using online calculators such as Mathway or Wolfram Alpha, or by working through practice problems in a textbook or online resource.

Q: What are some additional resources for learning about factorials?

A: Some additional resources for learning about factorials include:

  • Khan Academy: Khan Academy offers a comprehensive course on factorials and permutations.
  • Mathway: Mathway is an online calculator that can help you evaluate factorials and other mathematical expressions.
  • Wolfram Alpha: Wolfram Alpha is a powerful calculator that can help you evaluate factorials and other mathematical expressions.

Conclusion

Evaluating factorials can seem daunting at first, but with practice and patience, you can become proficient in solving these types of problems. Remember to always follow the order of operations and use the correct notation for factorials. By mastering factorials, you can unlock a world of mathematical possibilities and apply your skills to real-world problems.

Final Thoughts

Factorials are a fundamental concept in mathematics, and understanding how to evaluate them is crucial for solving various mathematical problems. By following the steps outlined in this article and practicing regularly, you can become a master of factorials and unlock a world of mathematical possibilities.