Number of Permutations of N Things taken All at once given R of them are Identical Solution

STEP 0: Pre-Calculation Summary
Formula Used
Number of Permutations = (Value of N!)/(Value of R!)
P = (n!)/(r!)
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 N - Value of N is any natural number or positive integer that can be used for combinatorial calculations.
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.
STEP 1: Convert Input(s) to Base Unit
Value of N: 8 --> No Conversion Required
Value of R: 4 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P = (n!)/(r!) --> (8!)/(4!)
Evaluating ... ...
P = 1680
STEP 3: Convert Result to Output's Unit
1680 --> No Conversion Required
FINAL ANSWER
1680 <-- Number of Permutations
(Calculation completed in 00.005 seconds)

Credits

Created by Mridul Sharma
Indian Institute of Information Technology (IIIT), Bhopal
Mridul Sharma has created this Calculator and 200+ more calculators!
Verified by Shweta Patil
Walchand College of Engineering (WCE), Sangli
Shweta Patil has verified this Calculator and 1100+ more calculators!

11 Linear Permutation Calculators

Number of Permutations of N Different Things taken R at once given M Specific Things Always Occur
Go Number of Permutations = Value of R!*(((Value of N-Value of M)!)/((Value of N-Value of R)!*(Value of R-Value of M)!))
Number of Permutations of N Different Things taken R at once given One Specific Thing Always Occurs
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 M Specific Things Never Occur
Go Number of Permutations = ((Value of N-Value of M)!)/((Value of N-Value of M-Value of R)!)
Number of Permutations of N Different Things taken Not More than R at once and Repetition Allowed
Go Number of Permutations = (Value of N*(Value of N^(Value of R)-1))/(Value of N-1)
Number of Permutations of N Different Things given M Specific Things Never Come Together
Go Number of Permutations = (Value of N!)-(Value of M!*(Value of N-Value of M+1)!)
Number of Permutations of N Different Things taken R at once given One Specific Thing Never Occurs
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
Go Number of Permutations = (Value of N!)/((Value of N-Value of R)!)
Number of Permutations of N Different Things given M Specific Things Always Come Together
Go Number of Permutations = Value of M!*(Value of N-Value of M+1)!
Number of Permutations of N Things taken All at once given R of them are Identical
Go Number of Permutations = (Value of N!)/(Value of R!)
Number of Permutations of N Different Things taken R at once and Repetition Allowed
Go Number of Permutations = Value of N^Value of R
Number of Permutations of N Different Things taken All at once
Go Number of Permutations = Value of N!

Number of Permutations of N Things taken All at once given R of them are Identical Formula

Number of Permutations = (Value of N!)/(Value of R!)
P = (n!)/(r!)

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 Things taken All at once given R of them are Identical?

Number of Permutations of N Things taken All at once given R of them are Identical calculator uses Number of Permutations = (Value of N!)/(Value of R!) to calculate the Number of Permutations, Number of Permutations of N Things taken All at once given R of them are Identical formula is defined as the total number of ways in which N objects can be arranged taken all at once when R objects out of N are the same. Number of Permutations is denoted by P symbol.

How to calculate Number of Permutations of N Things taken All at once given R of them are Identical using this online calculator? To use this online calculator for Number of Permutations of N Things taken All at once given R of them are Identical, enter Value of N (n) & Value of R (r) and hit the calculate button. Here is how the Number of Permutations of N Things taken All at once given R of them are Identical calculation can be explained with given input values -> 6720 = (8!)/(4!).

FAQ

What is Number of Permutations of N Things taken All at once given R of them are Identical?
Number of Permutations of N Things taken All at once given R of them are Identical formula is defined as the total number of ways in which N objects can be arranged taken all at once when R objects out of N are the same and is represented as P = (n!)/(r!) or Number of Permutations = (Value of N!)/(Value of R!). Value of N is any natural number or positive integer that can be used for combinatorial calculations & 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.
How to calculate Number of Permutations of N Things taken All at once given R of them are Identical?
Number of Permutations of N Things taken All at once given R of them are Identical formula is defined as the total number of ways in which N objects can be arranged taken all at once when R objects out of N are the same is calculated using Number of Permutations = (Value of N!)/(Value of R!). To calculate Number of Permutations of N Things taken All at once given R of them are Identical, you need Value of N (n) & Value of R (r). With our tool, you need to enter the respective value for Value of N & Value of R 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 N & Value of R. We can use 10 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 R!)*((Value of N-1)!)/((Value of N-Value of R)!*(Value of R-1)!)
  • Number of Permutations = ((Value of N-1)!)/((Value of N-1-Value of R)!)
  • Number of Permutations = Value of R!*(((Value of N-Value of M)!)/((Value of N-Value of R)!*(Value of R-Value of M)!))
  • Number of Permutations = ((Value of N-Value of M)!)/((Value of N-Value of M-Value of R)!)
  • Number of Permutations = Value of M!*(Value of N-Value of M+1)!
  • Number of Permutations = (Value of N!)-(Value of M!*(Value of N-Value of M+1)!)
  • Number of Permutations = Value of N^Value of R
  • Number of Permutations = (Value of N*(Value of N^(Value of R)-1))/(Value of N-1)
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