My maths is very rusty. I am looking to calculate how many unique combinations I can draw from a given set of names.
I understand the formula $\frac{n!}{(n-r)!(r)!}$ will give me the number of unique combinations of $r$ elements from the set with $n$ elements, where all combinations will contain at least $1$ different element.
What if I wanted to specify the minimum number of elements that had to be different?
For example, the number of combinations of $6$ names I could draw from $36$ names = $\frac{36!}{30!\,6!}=1,947,792$
Every combination would have at least 1 name different to every other combination. How do I work out the number of combinations if I wanted at least 2 or 3 names in every combination to be different.
Names in the set are unique and can't be repeated.
Thank you.
Best Answer
Unfortunately, the maximum number of combinations under such a restriction is not known in any closed-form manner. The topic of constructing combinations like this is the topic of Block Design. There is a theoretical maximum, but there's no guarantee that the maximum can be achieved for any particular number of chosen elements or number of elements available.