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

• TheRobsterUK
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.
TheRobsterUK
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

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:
$$A*B^{n}=A*(B^{n})$$
rather than [itex](A*B)^{n}[/tex]

Last edited:
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!

## 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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