Evaluate the combination:
14C7
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 = 14 and r = 7
| 14C7 2 | 14! |
| 7!(14 - 7)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 14!
14! = 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
14! = 87,178,291,200
Calculate (n - r)!:
(n - r)! = (14 - 7)!
(14 - 7)! = 7!
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
7! = 5,040
Calculate r!:
r! = 7!
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
7! = 5,040
Calculate 14C7
| 14C7 = | 87,178,291,200 |
| 5,040 x 5,040 |
| 14C7 = | 87,178,291,200 |
| 25,401,600 |
Final Answer
14C7 = 3,432
