No of Combinations of N Different Things taken R at once and Repetition Allowed Solution

STEP 0: Pre-Calculation Summary
Formula Used
Number of Combinations = C((Value of N+Value of R-1),Value of R)
C = C((n+r-1),r)
This formula uses 1 Functions, 3 Variables
Functions Used
C - In combinatorics, the binomial coefficient is a way to represent the number of ways to choose a subset of objects from a larger set. It is also known as the "n choose k" tool., C(n,k)
Variables Used
Number of Combinations - Number of Combinations is defined as the total number of unique arrangements that can be made from a set of items, without regard to the order of the items.
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
C = C((n+r-1),r) --> C((8+4-1),4)
Evaluating ... ...
C = 330
STEP 3: Convert Result to Output's Unit
330 --> No Conversion Required
FINAL ANSWER
330 <-- Number of Combinations
(Calculation completed in 00.004 seconds)

Credits

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Created by Divanshi Jain
Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka
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14 Combinations Calculators

No of Combinations of N Different Things taken R at once given M Specific Things Always Occur
​ Go Number of Combinations = C((Value of N-Value of M),(Value of R-Value of M))
No of Combinations of (P+Q) Things into Two Groups of P and Q Things
​ Go Number of Combinations = ((Value of P+Value of Q)!)/((Value of P!)*(Value of Q!))
nCr or C(n,r)
​ Go Number of Combinations = (Value of N!)/(Value of R!*(Value of N-Value of R)!)
Nth Catalan Number
​ Go Nth Catalan Number = (1/(Value of N+1))*C(2*Value of N,Value of N)
No of Combinations of N Identical Things into R Different Groups if Empty Groups are Allowed
​ Go Number of Combinations = C(Value of N+Value of R-1,Value of R-1)
No of Combinations of N Different Things taken R at once and Repetition Allowed
​ Go Number of Combinations = C((Value of N+Value of R-1),Value of R)
No of Combinations of N Different Things taken R at once given M Specific Things Never Occur
​ Go Number of Combinations = C((Value of N-Value of M),Value of R)
No of Combinations of N Different Things, P and Q Identical Things taken Atleast One at once
​ Go Number of Combinations = (Value of P+1)*(Value of Q+1)*(2^Value of N)-1
Maximum Value of nCr when N is Odd
​ Go Number of Combinations = C(Value of N (Odd),(Value of N (Odd)+1)/2)
No of Combinations of N Identical Things into R Different Groups if Empty Groups are Not Allowed
​ Go Number of Combinations = C(Value of N-1,Value of R-1)
Maximum Value of nCr when N is Even
​ Go Number of Combinations = C(Value of N,Value of N/2)
No of Combinations of N Different Things taken R at once
​ Go Number of Combinations = C(Value of N,Value of R)
No of Combinations of N Different Things taken Atleast One at once
​ Go Number of Combinations = 2^(Value of N)-1
No of Combinations of N Identical Things taken Zero or more at once
​ Go Number of Combinations = Value of N+1

No of Combinations of N Different Things taken R at once and Repetition Allowed Formula

Number of Combinations = C((Value of N+Value of R-1),Value of R)
C = C((n+r-1),r)

What are Combinations?

In combinatorics, Combinations refer to the different ways of selecting a subset of items from a larger set without regard to the order of selection. Combinations are used to count the number of possible outcomes when the order of selection does not matter. For example, if you have a set of three elements {A, B, C}, the Combinations of size 2 would be {AB, AC, BC}. In this case, the order of the items within each combination does not matter, so {AB} and {BA} are considered the same combination.

The number of Combinations of selecting "k" items from a set of "n" items is denoted as C(n, k). It is calculated using the binomial coefficient formula: C(n, k) = n! / (k! * (n - k)!)

Combinations have various applications in mathematics, probability theory, statistics, and other fields.

How to Calculate No of Combinations of N Different Things taken R at once and Repetition Allowed?

No of Combinations of N Different Things taken R at once and Repetition Allowed calculator uses Number of Combinations = C((Value of N+Value of R-1),Value of R) to calculate the Number of Combinations, The No of Combinations of N Different Things taken R at once and Repetition Allowed formula is defined as the total number of ways of selecting a collection of R objects from the given N different objects when repetition is allowed. Number of Combinations is denoted by C symbol.

How to calculate No of Combinations of N Different Things taken R at once and Repetition Allowed using this online calculator? To use this online calculator for No of Combinations of N Different Things taken R at once and Repetition Allowed, enter Value of N (n) & Value of R (r) and hit the calculate button. Here is how the No of Combinations of N Different Things taken R at once and Repetition Allowed calculation can be explained with given input values -> 120 = C((8+4-1),4).

FAQ

What is No of Combinations of N Different Things taken R at once and Repetition Allowed?
The No of Combinations of N Different Things taken R at once and Repetition Allowed formula is defined as the total number of ways of selecting a collection of R objects from the given N different objects when repetition is allowed and is represented as C = C((n+r-1),r) or Number of Combinations = C((Value of N+Value of R-1),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 No of Combinations of N Different Things taken R at once and Repetition Allowed?
The No of Combinations of N Different Things taken R at once and Repetition Allowed formula is defined as the total number of ways of selecting a collection of R objects from the given N different objects when repetition is allowed is calculated using Number of Combinations = C((Value of N+Value of R-1),Value of R). To calculate No of Combinations of N Different Things taken R at once and Repetition Allowed, 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 Combinations?
In this formula, Number of Combinations uses Value of N & Value of R. We can use 12 other way(s) to calculate the same, which is/are as follows -
  • Number of Combinations = C(Value of N,Value of R)
  • Number of Combinations = C((Value of N-Value of M),(Value of R-Value of M))
  • Number of Combinations = C((Value of N-Value of M),Value of R)
  • Number of Combinations = 2^(Value of N)-1
  • Number of Combinations = (Value of N!)/(Value of R!*(Value of N-Value of R)!)
  • Number of Combinations = Value of N+1
  • Number of Combinations = C(Value of N (Odd),(Value of N (Odd)+1)/2)
  • Number of Combinations = C(Value of N,Value of N/2)
  • Number of Combinations = (Value of P+1)*(Value of Q+1)*(2^Value of N)-1
  • Number of Combinations = ((Value of P+Value of Q)!)/((Value of P!)*(Value of Q!))
  • Number of Combinations = C(Value of N+Value of R-1,Value of R-1)
  • Number of Combinations = C(Value of N-1,Value of R-1)
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