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+29
What is the Answer?
a = 4.0278979798251E+29
How does the Ordered and Unordered Partitions Calculator work?
Free Ordered and Unordered Partitions Calculator - Given a population size (n) and a group population of (m), this calculator determines how many ordered or unordered groups of (m) can be formed from (n)
This calculator has 2 inputs.
This calculator has 2 inputs.
What 3 formulas are used for the Ordered and Unordered Partitions Calculator?
k = n/m
Unordered: a = n!/(k!)(m!k)
Ordered: a = n!/m!k
Unordered: a = n!/(k!)(m!k)
Ordered: a = n!/m!k
What 4 concepts are covered in the Ordered and Unordered Partitions Calculator?
- factorial
- The product of an integer and all the integers below it
- ordered partitions
- a list of pairwise disjoint nonempty subsets of s such that the union of these subsets is s.
- partition
- a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset.
- unordered partitions
- A partition is unordered when no distinction is made between subsets of the same size (the order of the subsets does not matter
