42 Combinations of 5 ·

26 Jul 2024, 00:00

Evaluate the combination:

42C5

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 = 42 and r = 5

42C5 2	42!
	5!(42 - 5)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 42!

42! = 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

42! = 1,405,006,117,752,879,788,779,635,797,590,784,832,178,972,610,527,232

Calculate (n - r)!:

(n - r)! = (42 - 5)!

(42 - 5)! = 37!

37! = 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

37! = 13,763,753,091,226,343,102,992,036,262,845,720,547,033,088

Calculate r!:

r! = 5!

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

5! = 120

Calculate 42C5

42C5 =	1,405,006,117,752,879,788,779,635,797,590,784,832,178,972,610,527,232
	120 x 13,763,753,091,226,343,102,992,036,262,845,720,547,033,088

42C5 =	1,405,006,117,752,879,788,779,635,797,590,784,832,178,972,610,527,232
	1,651,650,370,947,161,172,359,044,351,541,486,465,643,970,560

42C5 = 850,668

You have 1 free calculations remaining

Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(42,5)

What is the Answer?

42C5 = 850,668

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

42 Combinations of 5

Evaluate the combination: 42C5 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! = 42! 42! = 42 x 41 x 40 x 39 x 38 x 37 x 36