# Montmort’s matching problem with venn diagram

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.

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.

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]

quoted from rstudio

• You need to tell us what Montmort's matching problem is (by editing, not in the comments), because this is not common knowledge. Apr 15, 2022 at 15:44
• Seems you are asking about a derangement problem. And Venn Diagram is used to illustrate the relationship between various set - in probability we call them events. So you need to first determine the events you interested in to be shown in this Venn diagram. E.g. The events of card $1,2,3$ being matched. And then you place the singletons inside.
– BGM
Apr 15, 2022 at 20:28
• @ BGM, thank you for the reply. This is where is gets cloudy for me, there are $n=3$ with $n!$ permutations. If we use "pebble world" to describe the sample space, there are 3 pebbles and 6 sets within the space. [('1', '2', '3'), ('1', '3', '2'), ('2', '1', '3'), ('2', '3', '1'), ('3', '1', '2'), ('3', '2', '1')]. All the sets are overlapping, making it confusing for me to picture it in a venn diagram, hence, the question. Apr 16, 2022 at 5:40
• @Mike Earnest, thank you for the reply, i've added a shot description as suggested. Apr 16, 2022 at 5:53