l 8 Combinations of 2

Enter n

Enter r

  

Evaluate the combination:

8C2

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 = 8 and r = 2

8C2  2  8!
  2!(8 - 2)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 8!

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

8! = 40,320

Calculate (n - r)!:

(n - r)! = (8 - 2)!

(8 - 2)! = 6!

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

6! = 720

Calculate r!:

r! = 2!

2! = 2 x 1

2! = 2

Calculate 8C2

8C2  =  40,320
  2 x 720

8C2  =  40,320
  1,440

Final Answer


8C2 = 28