12 Combinations Of 6 - Math Celebrity

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Enter n

Enter r

Evaluate the combination:

12C6

Combination Definition:

A unique order or arrangement

Combination Formula:

nCr = n!
r!(n - r)!

where n is the number of itemsr is the unique arrangements.

Plug in n = 12 and r = 6

12C6 2 12!
6!(12 - 6)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 12!

12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

12! = 479,001,600

Calculate (n - r)!:

(n - r)! = (12 - 6)!

(12 - 6)! = 6!

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

6! = 720

Calculate r!:

r! = 6!

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

6! = 720

Calculate 12C6

12C6 = 479,001,600
720 x 720
12C6 = 479,001,600
518,400

Final Answer

12C6 = 924

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