l 15 Combinations of 5

Enter n

Enter r

  

Evaluate the combination:

15C5

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 = 15 and r = 5

15C5  2  15!
  5!(15 - 5)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 15!

15! = 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

15! = 1,307,674,368,000

Calculate (n - r)!:

(n - r)! = (15 - 5)!

(15 - 5)! = 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 r!:

r! = 5!

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

5! = 120

Calculate 15C5

15C5  =  1,307,674,368,000
  120 x 3,628,800

15C5  =  1,307,674,368,000
  435,456,000

Final Answer


15C5 = 3,003