Enter n

Enter r

  

Evaluate the combination:

20C10

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 = 20 and r = 10

20C10  2  20!
  10!(20 - 10)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 20!

20! = 20 x 19 x 18 x 17 x 16 x 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

20! = 2,432,902,008,176,640,000

Calculate (n - r)!:

(n - r)! = (20 - 10)!

(20 - 10)! = 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! = 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 20C10

20C10  =  2,432,902,008,176,640,000
  3,628,800 x 3,628,800

20C10  =  2,432,902,008,176,640,000
  13,168,189,440,000

Final Answer


20C10 = 184,756