Evaluate the combination:
16C16
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 = 16 and r = 16
| 16C16 2 | 16! |
| 16!(16 - 16)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 16!
16! = 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
16! = 20,922,789,888,000
Calculate (n - r)!:
(n - r)! = (16 - 16)!
(16 - 16)! = 0!
0! =
0! = 1
Calculate r!:
r! = 16!
16! = 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
16! = 20,922,789,888,000
Calculate 16C16
| 16C16 = | 20,922,789,888,000 |
| 20,922,789,888,000 x 1 |
| 16C16 = | 20,922,789,888,000 |
| 20,922,789,888,000 |
Final Answer
16C16 = 1
