l 11 Combinations of 3

Enter n

Enter r

  

Evaluate the combination:

11C3

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 = 11 and r = 3

11C3  2  11!
  3!(11 - 3)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 11!

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

11! = 39,916,800

Calculate (n - r)!:

(n - r)! = (11 - 3)!

(11 - 3)! = 8!

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

8! = 40,320

Calculate r!:

r! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate 11C3

11C3  =  39,916,800
  6 x 40,320

11C3  =  39,916,800
  241,920

Final Answer


11C3 = 165