The problem is as follows:
In an institution they offer three language courses one being German, the other French and the last one Polish. Four students enrolled in the three courses, six students in Polish and German and seven in French and Polish. If all students enrolled in Polish also enrolled in German or French. How many of the students were in the Polish course?
The existing alternatives in my book are:
What I tried to do is to build up a Venn diagram as shown below:
But from this point I am stuck as I do not know how to relate the number of students in Polish language since there is not known the total number of elements from all sets together.
Can this problem be solved without needing this information?.
There is one thing regarding how I understood the problem as it mentions seven students enrolled in French or Polish so by interpreting this information I assumed that $P=7$ and $F=7$ therefore the diagram would become into this:
By reviewing what it was mentioned in the problem I noticed that earlier assumptions did considered only elements belonging to $P$, $G$ or $F$ but it was not the case, therefore I changed this approach and "calculated" the elements for $G$ and $P$ and $G$ and $F$ alone being them $2$ and $3$ respectively.
This can be seen in the figure below:
But this is how far I went in the problem. How can I take it from here to reach the solution?.
Therefore I'm stuck at this, can somebody help me to go in the right track or what conclusion I have to take to solve this problem?