66 Combinations of 3 ·

26 Jul 2024, 00:00

Evaluate the combination:

66C3

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 = 66 and r = 3

66C3 2	66!
	3!(66 - 3)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 66!

66! = 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

66! = 544,344,939,077,443,069,445,496,060,275,635,856,761,283,034,568,718,387,417,404,234,993,819,829,995,466,026,946,857,533,440

Calculate (n - r)!:

(n - r)! = (66 - 3)!

(66 - 3)! = 63!

63! = 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

63! = 1,982,608,315,404,440,084,965,732,774,767,545,707,658,109,829,136,018,902,789,196,017,241,837,351,744,329,178,152,960

Calculate r!:

r! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate 66C3

66C3 =	544,344,939,077,443,069,445,496,060,275,635,856,761,283,034,568,718,387,417,404,234,993,819,829,995,466,026,946,857,533,440
	6 x 1,982,608,315,404,440,084,965,732,774,767,545,707,658,109,829,136,018,902,789,196,017,241,837,351,744,329,178,152,960

66C3 =	544,344,939,077,443,069,445,496,060,275,635,856,761,283,034,568,718,387,417,404,234,993,819,829,995,466,026,946,857,533,440
	11,895,649,892,426,641,393,217,929,037,797,439,037,597,409,346,275,371,330,477,124,541,260,503,171,269,075,715,227,648

66C3 = 45,760

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Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(66,3)

What is the Answer?

66C3 = 45,760

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

66 Combinations of 3

Evaluate the combination: 66C3 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! = 66! 66! = 66 x 65 x 64 x 63 x 62 x 61 x 60