69 Combinations of 5

Evaluate the combination:

69C5

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 = 69 and r = 5

69C5  2	69!
	5!(69 - 5)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 69!

69! = 69 x 68 x 67 x 66 x 65 x 64 x 63 x 62 x 61 x 60 x 59 x 58 x 57 x 56 x 55 x 54 x 53 x 52 x 51 x 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

69! = 171,122,452,428,141,297,375,735,434,272,073,448,876,652,721,480,628,511,030,304,905,066,123,383,956,194,496,253,690,059,725,733,888

Calculate (n - r)!:

(n - r)! = (69 - 5)!

(69 - 5)! = 64!

64! = 64 x 63 x 62 x 61 x 60 x 59 x 58 x 57 x 56 x 55 x 54 x 53 x 52 x 51 x 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

64! = 126,886,932,185,884,165,437,806,897,585,122,925,290,119,029,064,705,209,778,508,545,103,477,590,511,637,067,401,789,440

Calculate r!:

r! = 5!

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

5! = 120

Calculate 69C5

69C5  =	171,122,452,428,141,297,375,735,434,272,073,448,876,652,721,480,628,511,030,304,905,066,123,383,956,194,496,253,690,059,725,733,888
	120 x 126,886,932,185,884,165,437,806,897,585,122,925,290,119,029,064,705,209,778,508,545,103,477,590,511,637,067,401,789,440

69C5  =	171,122,452,428,141,297,375,735,434,272,073,448,876,652,721,480,628,511,030,304,905,066,123,383,956,194,496,253,690,059,725,733,888
	15,226,431,862,306,099,174,067,554,835,315,168,474,828,043,202,483,915,095,667,209,012,179,630,942,699,666,791,848,738,816

69C5 = 11,238,513

Excel or Google Sheets formula:

=COMBIN(69,5)

What is the Answer?

69C5 = 11,238,513

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

Example calculations for the Permutations and Combinations Calculator

Permutations and Combinations Calculator Video

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