SOLUTION: Out of a group of 50 companies, 18 have offices in Kenya, 26 have offices in Uganda and 26 have offices in Ethiopia. Furthermore, 11 have offices in Kenya and Uganda, 9 have office

Let K be the set and the number of the companies having offices in Kenya        (K = 18);
    G be the set and the number of the companies having offices in Uganda       (G = 26);
    E be the set and the number of the companies having offices in Ethiopia     (E = 26).


Do not worry that I denoted by the same symbol the set and the number: I made it for simplicity, 
and you always can distinct from the context what I am talking about.


Let KG be the intersection of the sets K and G and the number of elements in this set at the same time.

Let KE be the intersection of the sets K and E and the number of elements in this set at the same time.

Let GE be the intersection of the sets G and E and the number of elements in this set at the same time.

Let KGE be the intersection of the sets K, G and E and the number of elements in this set at the same time.


From the elementary theory of finite sets, we have this equation 

n(K U G U E) = K + G + E - KG - KE - GE + KGE.       (1)


By substituting the given number into this formula, you can find the number of elements n(K U G U E) in the set  K U G U E:

n(K U G U E) = 18 + 26 + 26 - 11 - 9 - 13 + 5 = 42. 


This number, 42, is the number of the companies that have the office at least in one of the three countries.

Then the number of companies, among the given 50, that HAVE NO offices in these countries, is 50 - 42 = 8.


So, we answered the first question.


Regarding the last question,  the answer is  K - KG - KE + KGE = 18 - 11 - 9 + 5 = 3.

So, exactly 3 of 50 companies have offices only in Kenya.