is how many ways could a class of 18 students divide into groups of 3 students each~ please leave full answers
Permutation and Combination Calculator
Number of Items is 18, Arrangements is 3. This is read as 18 choose 3.
If in fact I am incorrect in my assumption, and we need unique arrangements, press the combination button instead. That would be read as 18 choose 3 unique. That answer would be 816.
Either way will show you the math work for your answer
Think of it as having 18 people, 1-18. We take groups of 3, such as (1,2,3), (4,5,6), etc. For arrangements that do not need to be unique, (1,2,3) is considered different than (3,2,1). For unique arrangements, i.e., combinations, (1,2,3) is considered the same as (3,2,1) so that type is only counted once.
The wording of the question clearly implies that groups are not labeled. Therefore, this is known as unordered partition.
The answer is .
If the groups are labeled such, say by team names, then it is a ordered partition and the answer is .
Here is where I'm at right now.
Twelvefold way - Wikipedia, the free encyclopedia
Towards the bottom where it has S(n,x)
This is one of many cases in mathematics where terms have several uses.
What you are reading about, Stirling numbers, help in counting partitions of sets. But this problem is strictly about a partition of a set of 18 into cells of 3 each. The in general problem of partitions we consider how many ways to partition a set into nonempty, non-overlapping cells.
luckily, i have got it myself, but i did it in the long way, i didn't use the (3!)^6
because i just learn the staff of the permutation, that question is really tough_ thank you very much still ```