Answer
Success!
a = 4.0278979798251E+29
↓Steps Explained:↓
How many ways (unordered) can you:
Arrange 50 into groups of 10?
Calculate small groupings (k):
| k = | n |
| m |
| k = | 50 |
| 10 |
k = 5
Calculate unordered partitions (a):
| a = | n! |
| (k!)(m!k) |
| a = | 50! |
| (5!)(10!5) |
Calculate factorial
Remember our factorial lesson that:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
50!
50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5!
| a = | 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5! |
| 5!10!5 |
Cancelling 5!:
| a = | 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 |
| 10!5 |
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
10! = 3628800, so we have:
| a = | 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 |
| 36288005 |
| a = | 2.5345077668094E+62 |
| 6.292383221979E+32 |
Final Answer
a = 4.0278979798251E+29Related Calculators: Cox-Ross-Rubenstein Pricing | Permutations and Combinations Operations | Multifactorials