is it possible to have a venn diagram represent de Montmort matching problem where the number of cards is $n=3$ with the elements included in the diagram?
I understand how inclusion/exclusion works(thanks to the kind contributors here) with $ \bigcup_{i=1}^n A_i = \sum_{i=1}^n A_i - \sum_{i<j} A_i \cap A_j + \sum_{i<j<k} A_i \cap A_j \cap A_k - \dots + (-1)^{n+1} A_i \cap \dots A_n$.
However, i can't picture where the elements are placed in the venn diagram with 6 permutations of $n=3$. Feel free to expand the $n$ value if it helps represent the matching problem via the venn diagram.
Kindly advise. Thank you
added* description of Montmort’s matching problem
"Let there be $n$ objects numbered from 1 to $n$, and let them be ordered at random, assuming that the $n!$ permutations are equally probable. A coincidence occurs if object number $i$ is found at the $i$th place. The problem is to find the number of permutations with at least one coincidence or, equivalently, the probability of at least one coincidence...:"[A. Hald]
Here is the finest Venn diagram that Windows paint can offer: