Evaluate the combination:
10C4
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 = 4
| 10C4 2 | 10! |
| 4!(10 - 4)! |
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 - 4)!
(10 - 4)! = 6!
6! = 6 x 5 x 4 x 3 x 2 x 1
6! = 720
Calculate r!:
r! = 4!
4! = 4 x 3 x 2 x 1
4! = 24
Calculate 10C4
| 10C4 = | 3,628,800 |
| 24 x 720 |
| 10C4 = | 3,628,800 |
| 17,280 |
Final Answer
10C4 = 210
