Evaluate the combination:
9C4
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 = 9 and r = 4
| 9C4 2 | 9! |
| 4!(9 - 4)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 9!
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
9! = 362,880
Calculate (n - r)!:
(n - r)! = (9 - 4)!
(9 - 4)! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120
Calculate r!:
r! = 4!
4! = 4 x 3 x 2 x 1
4! = 24
Calculate 9C4
| 9C4 = | 362,880 |
| 24 x 120 |
| 9C4 = | 362,880 |
| 2,880 |
Final Answer
9C4 = 126
