l 10 Combinations of 3

Enter n

Enter r

  

Evaluate the combination:

10C3

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 = 10 and r = 3

10C3  2  10!
  3!(10 - 3)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 10!

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

10! = 3,628,800

Calculate (n - r)!:

(n - r)! = (10 - 3)!

(10 - 3)! = 7!

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

7! = 5,040

Calculate r!:

r! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate 10C3

10C3  =  3,628,800
  6 x 5,040

10C3  =  3,628,800
  30,240

Final Answer


10C3 = 120