40 Combinations of 2

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Evaluate the combination:

40C2

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 = 40 and r = 2
40C2  2  40!
  2!(40 - 2)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 40!

40! = 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

40! = 815,915,283,247,897,683,795,548,521,301,193,790,359,984,930,816

Calculate (n - r)!:

(n - r)! = (40 - 2)!

(40 - 2)! = 38!

38! = 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

38! = 523,022,617,466,601,037,913,697,377,988,137,380,787,257,344

Calculate r!:

r! = 2!

2! = 2 x 1

2! = 2

Calculate 40C2
40C2  =  815,915,283,247,897,683,795,548,521,301,193,790,359,984,930,816
  2 x 523,022,617,466,601,037,913,697,377,988,137,380,787,257,344

40C2  =  815,915,283,247,897,683,795,548,521,301,193,790,359,984,930,816
  1,046,045,234,933,202,075,827,394,755,976,274,761,574,514,688

40C2 = 780

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Excel or Google Sheets formula:
Excel or Google Sheets formula:=COMBIN(40,2)

What is the Answer?

40C2 = 780

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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