33 Combinations of 4

Publish date: 2024-06-24
Image to Crop

Evaluate the combination:

33C4

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 = 33 and r = 4
33C4  2  33!
  4!(33 - 4)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 33!

33! = 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 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

33! = 8,683,317,618,811,885,938,715,673,895,318,323,200

Calculate (n - r)!:

(n - r)! = (33 - 4)!

(33 - 4)! = 29!

29! = 29 x 28 x 27 x 26 x 25 x 24 x 23 x 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

29! = 8,841,761,993,739,700,772,720,181,510,144

Calculate r!:

r! = 4!

4! = 4 x 3 x 2 x 1

4! = 24

Calculate 33C4
33C4  =  8,683,317,618,811,885,938,715,673,895,318,323,200
  24 x 8,841,761,993,739,700,772,720,181,510,144

33C4  =  8,683,317,618,811,885,938,715,673,895,318,323,200
  212,202,287,849,752,818,545,284,356,243,456

33C4 = 40,920

You have 1 free calculations remaining


Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(33,4)

What is the Answer?

33C4 = 40,920

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

ncG1vNJzZmivp6x7rq3ToZqepJWXv6rA2GeaqKVfpbKzudStmK2hn6N7sbTPeKWupW1ogGewxKd0bV6goYqEu8yboKeZpJ68r78%3D