Factorial Question | Solve k(n-1)! Equation

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In summary, the conversation discusses the use of factorials in an equation and the convention used to save parentheses in expressions involving a power. It also clarifies that the terms (k(n-1))! and k((n-1)!) cannot be misunderstood. The convention used is similar to the one used with expressions involving a power.
  • #1
TheRobsterUK
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Hi,

I have a question about factorials that I'm hoping someone can help me with.

I know that the factorial n! means the product of the integers from 1 to n, for example if I have 4! then this is equal to 4 x 3 x 2 x 1 = 24, but I have an equation which contains the term:

k(n-1)!

I am not sure how to interpret this...for instance, if we assume that k=4 and n=8, does this give:

4(8-1)!
= 4 x 7!
= 4 x 5,040
= 20,160

Or does it give:

4(8-1)!
=4 x 7!
=28!
=3.0489 x 10^29

I'm guessing it's the first one but am not sure...can someone confirm or provide the correct answer please?

Many Thanks
-Rob
 
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  • #2
Note that the notations:
(k(n-1))!, k((n-1)!) CANNOT be misunderstood.

The convention used, in order to save parentheses is:
k(n-1)!=k((n-1)!).

Note that this convention is akin to the one used with expressions involving a power:
[tex]A*B^{n}=A*(B^{n})[/tex]
rather than [itex](A*B)^{n}[/tex]
 
Last edited:
  • #3
in

Hi Robin,

You are correct in your assumption that the first interpretation is the correct one. The factorial operation is distributive, meaning it can be applied to individual factors within a product. So in this case, k(n-1)! can be rewritten as k x (n-1)! and then evaluated as 4 x 7! as you did. The second interpretation would be incorrect as it would result in a much larger number than the first one.

Hope this helps clarify your doubt. Keep practicing with factorials and you'll become more comfortable with them. Good luck!

 

Related to Factorial Question | Solve k(n-1)! Equation

1. What is a factorial?

A factorial is a mathematical operation denoted by an exclamation mark (!) after a number. It represents the product of all positive integers from 1 to that number. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

2. How do you solve a factorial equation?

To solve a factorial equation, you need to determine the value of the number inside the parentheses first. Then, you can use a calculator or manually calculate the product of all the positive integers from 1 to that number. Finally, you can substitute the value of the factorial into the equation and solve for the variable.

3. What does k(n-1)! mean?

k(n-1)! is a factorial equation where k is a variable and (n-1)! represents the product of all positive integers from 1 to n-1. This equation can be solved by determining the value of (n-1)! and substituting it into the equation to solve for k.

4. Can you solve a factorial equation with decimals or negative numbers?

No, factorial equations are only defined for positive integers. They cannot be solved with decimals or negative numbers.

5. What is the significance of factorial equations in science?

Factorial equations are commonly used in statistics and probability to calculate the number of possible combinations or permutations of a given set of elements. They also have applications in physics, engineering, and computer science for solving various problems and equations.

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