40 Combinations of 3

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Evaluate the combination:

₄₀C₃

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 = 3

40C3  2	40!
	3!(40 - 3)!

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 - 3)!

(40 - 3)! = 37!

37! = 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

37! = 13,763,753,091,226,343,102,992,036,262,845,720,547,033,088

Calculate r!:

r! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate ₄₀C₃

40C3  =	815,915,283,247,897,683,795,548,521,301,193,790,359,984,930,816
	6 x 13,763,753,091,226,343,102,992,036,262,845,720,547,033,088

40C3  =	815,915,283,247,897,683,795,548,521,301,193,790,359,984,930,816
	82,582,518,547,358,058,617,952,217,577,074,323,282,198,528

₄₀C₃ = 9,880

You have 1 free calculations remaining

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Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(40,3)

What is the Answer?

₄₀C₃ = 9,880

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 = _nP_r
Number of combination(s) of n items arranged in r unique ways = _nC_r 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?

combination

a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter
_nP_r = n!/r!(n - r)!

factorial

The product of an integer and all the integers below it

permutation

a way in which a set or number of things can be ordered or arranged.
_nP_r = n!/(n - r)!

permutations and combinations

Example calculations for the Permutations and Combinations Calculator

Permutations and Combinations Calculator Video

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