17 Combinations of 3 ·

11 Jun 2024, 00:00

Evaluate the combination:

17C3

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 = 17 and r = 3

17C3 2	17!
	3!(17 - 3)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 17!

17! = 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

17! = 355,687,428,096,000

Calculate (n - r)!:

(n - r)! = (17 - 3)!

(17 - 3)! = 14!

14! = 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

14! = 87,178,291,200

Calculate r!:

r! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate 17C3

17C3 =	355,687,428,096,000
	6 x 87,178,291,200

17C3 =	355,687,428,096,000
	523,069,747,200

17C3 = 680

Excel or Google Sheets formula:

=COMBIN(17,3)

What is the Answer?

17C3 = 680

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

17 Combinations of 3

Evaluate the combination: 17C3 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! = 17! 17! = 17 x 16 x 15 x 14 x 13 x 12 x 11