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 = 126
What is the Answer?
a = 126
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
