22 Combinations of 3

Publish date: 2024-05-06
22 Combinations of 3

22 Combinations of 3

Image to Crop

Evaluate the combination:

22C3

Combination Definition:

A unique order or arrangement

Combination Formula:
nCr  =  n!
  r!(n - r)!

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

Plug in n = 22 and r = 3
22C3  2  22!
  3!(22 - 3)!

Factorial Formula:

n! = n * (n - 1) * (n - 2) * .... * 2 * 1

Calculate the numerator n!:

n! = 22!

22! = 22 x 21 x 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

22! = 1,124,000,727,777,607,680,000

Calculate (n - r)!:

(n - r)! = (22 - 3)!

(22 - 3)! = 19!

19! = 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

19! = 121,645,100,408,832,000

Calculate r!:

r! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate 22C3
22C3  =  1,124,000,727,777,607,680,000
  6 x 121,645,100,408,832,000

22C3  =  1,124,000,727,777,607,680,000
  729,870,602,452,992,000

22C3 = 1,540


Excel or Google Sheets formula:

=COMBIN(22,3)

What is the Answer?

22C3 = 1,540

How does the Permutations and Combinations Calculator work?

Free Permutations and Combinations Calculator - 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?

nPr=n!/r!
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?

combinationa 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)!factorialThe product of an integer and all the integers below itpermutationa way in which a set or number of things can be ordered or arranged.
nPr = n!/(n - r)!permutations and combinations

Example calculations for the Permutations and Combinations Calculator

Permutations and Combinations Calculator Video


Tags:

Add This Calculator To Your Website

ncG1vNJzZmivp6x7rq3ToZqepJWXv6rA2GeaqKVfpbKzudStmK2hn6N7sbTPeKWupW1nf2ewxKd0bF6goYqEu8yboKeZpJ68r78%3D