How many ways (ordered) can you:
Arrange 18 into groups of 6?
Calculate small groupings (k):
| k = | n |
| m |
| k = | 18 |
| 6 |
k = 3
Calculate ordered partitions (a):
| a = | n! |
| m!k |
| a = | 18! |
| 6!3 |
Calculate factorial
Remember our factorial lesson that:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Plug in n = 18
18! = 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 x 4 x 3 x 2 x 1
18! = 6402373705728000
6! = 6 x 5 x 4 x 3 x 2 x 1
6! = 720, so we have:
| a = | 18! |
| 7203 |
| a = | 6402373705728000 |
| 373248000 |
Final Answer
a = 17153136
What is the Answer?
a = 17153136
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
