50 Combinations of 7 ·

13 Jun 2024, 00:00

Evaluate the combination:

50C7

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 = 50 and r = 7

50C7 2	50!
	7!(50 - 7)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 50!

50! = 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

50! = 30,414,093,201,713,375,576,366,966,406,747,986,832,057,064,836,514,787,179,557,289,984

Calculate (n - r)!:

(n - r)! = (50 - 7)!

(50 - 7)! = 43!

43! = 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

43! = 60,415,263,063,373,834,074,440,829,285,578,945,930,237,590,418,489,344

Calculate r!:

r! = 7!

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

7! = 5,040

Calculate 50C7

50C7 =	30,414,093,201,713,375,576,366,966,406,747,986,832,057,064,836,514,787,179,557,289,984
	5,040 x 60,415,263,063,373,834,074,440,829,285,578,945,930,237,590,418,489,344

50C7 =	30,414,093,201,713,375,576,366,966,406,747,986,832,057,064,836,514,787,179,557,289,984
	304,492,925,839,404,120,332,358,110,389,933,252,854,651,381,391,504,179,200

50C7 = 99,884,400

Excel or Google Sheets formula:

=COMBIN(50,7)

What is the Answer?

50C7 = 99,884,400

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

50 Combinations of 7

Evaluate the combination: 50C7 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! = 50! 50! = 50 x 49 x 48 x 47 x 46 x 45 x 44