20 Combinations of 7 ·

13 Jul 2024, 00:00

Evaluate the combination:

20C7

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 = 20 and r = 7

20C7 2	20!
	7!(20 - 7)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 20!

20! = 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

20! = 2,432,902,008,176,640,000

Calculate (n - r)!:

(n - r)! = (20 - 7)!

(20 - 7)! = 13!

13! = 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

13! = 6,227,020,800

Calculate r!:

r! = 7!

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1

7! = 5,040

Calculate 20C7

20C7 =	2,432,902,008,176,640,000
	5,040 x 6,227,020,800

20C7 =	2,432,902,008,176,640,000
	31,384,184,832,000

20C7 = 77,520

Excel or Google Sheets formula:

=COMBIN(20,7)

What is the Answer?

20C7 = 77,520

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

20 Combinations of 7

Evaluate the combination: 20C7 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! = 20! 20! = 20 x 19 x 18 x 17 x 16 x 15 x 14