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Evaluate the combination:

₄₅C₆

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 = 45 and r = 6

45C6  2	45!
	6!(45 - 6)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 45!

45! = 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

45! = 119,622,220,865,480,188,574,992,723,157,469,373,503,186,265,858,579,103,744

Calculate (n - r)!:

(n - r)! = (45 - 6)!

(45 - 6)! = 39!

39! = 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

39! = 20,397,882,081,197,441,587,828,472,941,238,084,160,318,341,120

Calculate r!:

r! = 6!

6! = 6 x 5 x 4 x 3 x 2 x 1

6! = 720

Calculate ₄₅C₆

45C6  =	119,622,220,865,480,188,574,992,723,157,469,373,503,186,265,858,579,103,744
	720 x 20,397,882,081,197,441,587,828,472,941,238,084,160,318,341,120

45C6  =	119,622,220,865,480,188,574,992,723,157,469,373,503,186,265,858,579,103,744
	14,686,475,098,462,158,957,356,980,700,274,941,792,791,769,907,200

₄₅C₆ = 8,145,060

You have 1 free calculations remaining

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Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(45,6)

What is the Answer?

₄₅C₆ = 8,145,060

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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