l 5 Combinations of 3

Enter n

Enter r

  

Answer
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5C3 = 10

↓Steps Explained:↓



Evaluate the combination:

5C3

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 = 5 and r = 3

5C3  2  5!
  3!(5 - 3)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 5!

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

5! = 120

Calculate (n - r)!:

(n - r)! = (5 - 3)!

(5 - 3)! = 2!

2! = 2 x 1

2! = 2

Calculate r!:

r! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate 5C3

5C3  =  120
  6 x 2

5C3  =  120
  12

Final Answer

5C3 = 10

Related Calculators:  Factorials  |  Multiplication Property Of Inequality  |  Multiplication Array
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