Evaluate the combination:
10C5
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 = 5
| 10C5 2 | 10! |
| 5!(10 - 5)! |
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 - 5)!
(10 - 5)! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120
Calculate r!:
r! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120
Calculate 10C5
| 10C5 = | 3,628,800 |
| 120 x 120 |
| 10C5 = | 3,628,800 |
| 14,400 |
Final Answer
10C5 = 252
