12 Combinations Of 3 - Math Celebrity

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Answer
Success!12C3 = 220

↓Steps Explained:↓

Evaluate the combination:

12C3

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 = 3

12C3 2 12!
3!(12 - 3)!

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 - 3)!

(12 - 3)! = 9!

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

9! = 362,880

Calculate r!:

r! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate 12C3

12C3 = 479,001,600
6 x 362,880
12C3 = 479,001,600
2,177,280

Final Answer

12C3 = 220Take the Quiz Switch to Chat ModeRelated Calculators: Boolean Algebra Multiplication |

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