Finding the number of female white tigers with a Venn Diagram. [closed]

The question goes: In a Zoo, there are 6 Bengal white tigers and 7 Bengal royal tigers. Out of these tigers, 5 are males and 10 are either Bengal royal tigers or males. Find the number of female Bengal white tigers in the Zoo.

As per my understanding, there are four possible sets here: sets of Bengal white, Bengal Royal, Male and female tigers respectively. The only given data I find here n(BW)=6, n(BR)=7, n(M)=5, n(BR U M) =10, n(FBW)=?

Please give me some hints on how to start solving these kinds of problems (related to cardinality) where the given data at first glance seems too insufficient.

Solution 1:

The number of female royal tigers is $10-5=5$, since "royal or male" completely includes "male" – we are taking set difference here. Then a simple chain of arithmetic gives us $7-5=2$ male royals, $5-2=3$ male whites and $6-3=3$ female whites.

Implicit in the question statement is that all objects of interest are either white or royal and either male or female.