5 Combinations of 20

Enter your n and r values below:

<-- Enter Number of Items (n)
<-- Enter Number of Arrangements (r)

  

Evaluate the combination nCr
A combination is a way to order or arrange a set or number of things (uniquely)
The formula for a combination of choosing r unique ways from n possibilities is:
nCr  =  n!
  r!(n - r)!

where n is the number of items and r is the unique arrangements.

Plugging in our numbers of n = 5 and r = 20, we get

5C20  =  5!
  20!(5 - 20)!

Remember from our factorial lesson that n! = n * (n - 1) * (n - 2) * .... * 2 * 1

Calculate the numerator n!:

n! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120

Calculate the first denominator (n - r)!:

(n - r)! = (5 - 20)!
(5 - 20)! = -15!
-15! =
-15! = 1

Calculate the second denominator r!:

r! = 20!
20! = 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
20! = 2,432,902,008,176,640,000

Calculate our combination value nCr for n = 5 and r = 20

5C20  =  120
  2,432,902,008,176,640,000 x 1

5C20  =  120
  2,432,902,008,176,640,000

5C20 = 0





In Microsoft Excel or Google Sheets, you write this function as =COMBIN(5,20)


What is the Answer?

5C20 = 0

How does the Permutations and Combinations Calculator work?

Calculates the following:
Number of permutation(s) of n items arranged in r ways = nPr
Number of combination(s) of n items arranged in r unique ways = nCr including subsets of sets
This calculator has 2 inputs.

What 2 formulas are used for the Permutations and Combinations Calculator?

  1. nPr=n!/r!
  2. nCr=n!/r!(n-r)!

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Permutations and Combinations Calculator?

combination
a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter
nPr = n!/r!(n - r)!
factorial
The product of an integer and all the integers below it
permutation
a way in which a set or number of things can be ordered or arranged.
nPr = n!/(n - r)!
permutations and combinations

What are some example calculations for the Permutations and Combinations Calculator?

  1. 10 permutations of 6
  2. 5 combinations of 3
  3. 9 combination 4
  4. 8 combination 2
  5. 6 permutation 2
  6. 10 permutations of 5
  7. 6P3
  8. 7c4
  9. how many subsets of at least 3 elements can be formed from a set of 4 elements

Permutations and Combinations Calculator Video


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