Evaluate the combination:

32C4

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 = 32 and r = 4

32C4  2	32!
	4!(32 - 4)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 32!

32! = 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

32! = 263,130,836,933,693,517,766,352,317,727,113,216

Calculate (n - r)!:

(n - r)! = (32 - 4)!

(32 - 4)! = 28!

28! = 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

28! = 304,888,344,611,713,836,734,530,715,648

Calculate r!:

r! = 4!

4! = 4 x 3 x 2 x 1

4! = 24

Calculate 32C4

32C4  =	263,130,836,933,693,517,766,352,317,727,113,216
	24 x 304,888,344,611,713,836,734,530,715,648

32C4  =	263,130,836,933,693,517,766,352,317,727,113,216
	7,317,320,270,681,131,518,678,783,754,240

32C4 = 35,960

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Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(32,4)

What is the Answer?

32C4 = 35,960

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

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