30 Combinations of 2

Evaluate the combination:

30C2

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 = 30 and r = 2

30C2 2	30!
	2!(30 - 2)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 30!

30! = 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

30! = 265,252,859,812,191,032,188,804,700,045,312

Calculate (n - r)!:

(n - r)! = (30 - 2)!

(30 - 2)! = 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! = 2!

2! = 2 x 1

2! = 2

Calculate 30C2

30C2 =	265,252,859,812,191,032,188,804,700,045,312
	2 x 304,888,344,611,713,836,734,530,715,648

30C2 =	265,252,859,812,191,032,188,804,700,045,312
	609,776,689,223,427,673,469,061,431,296

30C2 = 435

Excel or Google Sheets formula:

=COMBIN(30,2)

What is the Answer?

30C2 = 435

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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