Answer
a = 126
↓Steps Explained:↓
How many ways (unordered) can you:
Arrange 10 into groups of 5?
Calculate small groupings (k):
| k = | n |
| m |
| k = | 10 |
| 5 |
k = 2
Calculate unordered partitions (a):
| a = | n! |
| (k!)(m!k) |
| a = | 10! |
| (2!)(5!2) |
Calculate factorial
Remember our factorial lesson that:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
10!
10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2!
| a = | 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2! |
| 2!5!2 |
Cancelling 2!:
| a = | 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 |
| 5!2 |
5! = 5 x 4 x 3 x 2 x 1
5! = 120, so we have:
| a = | 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 |
| 1202 |
| a = | 1814400 |
| 14400 |
Final Answer
a = 126Related Calculators: Cox-Ross-Rubenstein Pricing | Permutations and Combinations Operations | Multifactorials