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
You have 2 free calculationss remaining
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
For more math formulas, check out our Formula Dossier
Unordered: a = n!/(k!)(m!k)
Ordered: a = n!/m!k
For more math formulas, check out our Formula Dossier
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
Example calculations for the Ordered and Unordered Partitions Calculator
Ordered and Unordered Partitions Calculator Video
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