100 Combinations of 2 ·

10 Jul 2024, 00:00

Evaluate the combination:

100C2

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 = 100 and r = 2

100C2 2	100!
	2!(100 - 2)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 100!

100! = 100 x 99 x 98 x 97 x 96 x 95 x 94 x 93 x 92 x 91 x 90 x 89 x 88 x 87 x 86 x 85 x 84 x 83 x 82 x 81 x 80 x 79 x 78 x 77 x 76 x 75 x 74 x 73 x 72 x 71 x 70 x 69 x 68 x 67 x 66 x 65 x 64 x 63 x 62 x 61 x 60 x 59 x 58 x 57 x 56 x 55 x 54 x 53 x 52 x 51 x 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 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

100! = 93,326,215,443,944,102,188,325,606,108,575,267,240,944,254,854,960,571,509,166,910,400,407,995,064,242,937,148,632,694,030,450,512,898,042,989,296,944,474,898,258,737,204,311,236,641,477,561,877,016,501,813,248

Calculate (n - r)!:

(n - r)! = (100 - 2)!

(100 - 2)! = 98!

98! = 98 x 97 x 96 x 95 x 94 x 93 x 92 x 91 x 90 x 89 x 88 x 87 x 86 x 85 x 84 x 83 x 82 x 81 x 80 x 79 x 78 x 77 x 76 x 75 x 74 x 73 x 72 x 71 x 70 x 69 x 68 x 67 x 66 x 65 x 64 x 63 x 62 x 61 x 60 x 59 x 58 x 57 x 56 x 55 x 54 x 53 x 52 x 51 x 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 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

98! = 9,426,890,448,883,242,029,410,148,360,874,034,376,137,592,466,180,063,696,357,188,182,614,769,297,217,373,775,790,759,257,383,412,737,431,326,439,501,183,709,769,874,985,637,770,333,212,700,442,263,289,856

Calculate r!:

r! = 2!

2! = 2 x 1

2! = 2

Calculate 100C2

100C2 =	93,326,215,443,944,102,188,325,606,108,575,267,240,944,254,854,960,571,509,166,910,400,407,995,064,242,937,148,632,694,030,450,512,898,042,989,296,944,474,898,258,737,204,311,236,641,477,561,877,016,501,813,248
	2 x 9,426,890,448,883,242,029,410,148,360,874,034,376,137,592,466,180,063,696,357,188,182,614,769,297,217,373,775,790,759,257,383,412,737,431,326,439,501,183,709,769,874,985,637,770,333,212,700,442,263,289,856

100C2 =	93,326,215,443,944,102,188,325,606,108,575,267,240,944,254,854,960,571,509,166,910,400,407,995,064,242,937,148,632,694,030,450,512,898,042,989,296,944,474,898,258,737,204,311,236,641,477,561,877,016,501,813,248
	18,853,780,897,766,484,058,820,296,721,748,068,752,275,184,932,360,127,392,714,376,365,229,538,594,434,747,551,581,518,514,766,825,474,862,652,879,002,367,419,539,749,971,275,540,666,425,400,884,526,579,712

100C2 = 4,950

Excel or Google Sheets formula:

=COMBIN(100,2)

What is the Answer?

100C2 = 4,950

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

100 Combinations of 2

Evaluate the combination: 100C2 A unique order or arrangement where n is the number of itemsr is the unique arrangements. n! = n * (n - 1) * (n - 2) * .... * 2 * 1 n! = 100! 100! = 100 x 99 x 98 x 97 x 96 x 95 x 94