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Evaluate the combination:

₄₉C₇

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 = 49 and r = 7

49C7  2	49!
	7!(49 - 7)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 49!

49! = 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

49! = 608,281,864,034,267,522,488,601,608,116,731,623,168,777,542,102,418,391,010,639,872

Calculate (n - r)!:

(n - r)! = (49 - 7)!

(49 - 7)! = 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 r!:

r! = 7!

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

7! = 5,040

Calculate ₄₉C₇

49C7  =	608,281,864,034,267,522,488,601,608,116,731,623,168,777,542,102,418,391,010,639,872
	5,040 x 1,405,006,117,752,879,788,779,635,797,590,784,832,178,972,610,527,232

49C7  =	608,281,864,034,267,522,488,601,608,116,731,623,168,777,542,102,418,391,010,639,872
	7,081,230,833,474,513,888,212,957,203,863,203,194,073,908,744,913,158,144

₄₉C₇ = 85,900,584

You have 1 free calculations remaining

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Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(49,7)

What is the Answer?

₄₉C₇ = 85,900,584

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 = _nP_r
Number of combination(s) of n items arranged in r unique ways = _nC_r 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?

combination

a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter
_nP_r = n!/r!(n - r)!

factorial

The product of an integer and all the integers below it

permutation

a way in which a set or number of things can be ordered or arranged.
_nP_r = n!/(n - r)!

permutations and combinations

Example calculations for the Permutations and Combinations Calculator

Permutations and Combinations Calculator Video

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