Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs Solution

STEP 0: Pre-Calculation Summary
Formula Used
Number of Permutations = (Value of R!)*((Value of N-1)!)/((Value of N-Value of R)!*(Value of R-1)!)
P = (r!)*((n-1)!)/((n-r)!*(r-1)!)
This formula uses 3 Variables
Variables Used
Number of Permutations - Number of Permutations is the number of distinct arrangements that are possible using 'N' things following a given condition.
Value of R - Value of R is the number of things that are selected for Permutation or Combination out of a given set of 'N' things, and it should be always less than n.
Value of N - Value of N is any natural number or positive integer that can be used for combinatorial calculations.
STEP 1: Convert Input(s) to Base Unit
Value of R: 4 --> No Conversion Required
Value of N: 8 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P = (r!)*((n-1)!)/((n-r)!*(r-1)!) --> (4!)*((8-1)!)/((8-4)!*(4-1)!)
Evaluating ... ...
P = 840
STEP 3: Convert Result to Output's Unit
840 --> No Conversion Required
FINAL ANSWER
840 <-- Number of Permutations
(Calculation completed in 00.004 seconds)

Credits

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Created by Mridul Sharma
Indian Institute of Information Technology (IIIT), Bhopal
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Verified by Shweta Patil
Walchand College of Engineering (WCE), Sangli
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Linear Permutation Calculators

Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs
​ LaTeX ​ Go Number of Permutations = (Value of R!)*((Value of N-1)!)/((Value of N-Value of R)!*(Value of R-1)!)
Number of Permutations of N Different Things taken R at once given One Specific Thing Never Occurs
​ LaTeX ​ Go Number of Permutations = ((Value of N-1)!)/((Value of N-1-Value of R)!)
Number of Permutations of N Different Things taken R at once
​ LaTeX ​ Go Number of Permutations = (Value of N!)/((Value of N-Value of R)!)
Number of Permutations of N Different Things taken All at once
​ LaTeX ​ Go Number of Permutations = Value of N!

Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs Formula

​LaTeX ​Go
Number of Permutations = (Value of R!)*((Value of N-1)!)/((Value of N-Value of R)!*(Value of R-1)!)
P = (r!)*((n-1)!)/((n-r)!*(r-1)!)

What is Permutation?

In mathematics, a permutation is an arrangement of a set of objects in a specific order. For example, if the set of objects is {1, 2, 3}, then the possible permutations are:

(1, 2, 3)
(1, 3, 2)
(2, 1, 3)
(2, 3, 1)
(3, 1, 2)
(3, 2, 1)

The number of permutations of a set of n objects is given by n!, which is the product of all the positive integers from 1 to n.

Permutations can be used to describe the possible arrangements of elements in a set, and they have a wide range of applications in various areas of mathematics and other fields.

How to Calculate Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs?

Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs calculator uses Number of Permutations = (Value of R!)*((Value of N-1)!)/((Value of N-Value of R)!*(Value of R-1)!) to calculate the Number of Permutations, Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs formula is defined as the total number of ways in which R different things from the given N things can be arranged such that one specific thing always occurs in the arrangement. Number of Permutations is denoted by P symbol.

How to calculate Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs using this online calculator? To use this online calculator for Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs, enter Value of R (r) & Value of N (n) and hit the calculate button. Here is how the Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs calculation can be explained with given input values -> 126 = (4!)*((8-1)!)/((8-4)!*(4-1)!).

FAQ

What is Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs?
Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs formula is defined as the total number of ways in which R different things from the given N things can be arranged such that one specific thing always occurs in the arrangement and is represented as P = (r!)*((n-1)!)/((n-r)!*(r-1)!) or Number of Permutations = (Value of R!)*((Value of N-1)!)/((Value of N-Value of R)!*(Value of R-1)!). Value of R is the number of things that are selected for Permutation or Combination out of a given set of 'N' things, and it should be always less than n & Value of N is any natural number or positive integer that can be used for combinatorial calculations.
How to calculate Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs?
Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs formula is defined as the total number of ways in which R different things from the given N things can be arranged such that one specific thing always occurs in the arrangement is calculated using Number of Permutations = (Value of R!)*((Value of N-1)!)/((Value of N-Value of R)!*(Value of R-1)!). To calculate Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs, you need Value of R (r) & Value of N (n). With our tool, you need to enter the respective value for Value of R & Value of N and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Number of Permutations?
In this formula, Number of Permutations uses Value of R & Value of N. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Number of Permutations = Value of N!
  • Number of Permutations = (Value of N!)/((Value of N-Value of R)!)
  • Number of Permutations = ((Value of N-1)!)/((Value of N-1-Value of R)!)
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