Answer :

There were four portions of warden pie and four portions of venison pasty to be distributed among eight out of eleven guests. 

But five out of the eleven will only eat the pie, four will only eat the pasty, and two are willing to eat of either. 

Any possible combination must fall into one of the following groups. 

(i.) Where the warden pie is distributed entirely among the five first mentioned; 
(ii.) where only one of the accommodating pair is given pie; 
(iii.) where the other of the pair is given pie; 
(iv.) where both of the pair are given pie. 

The numbers of combinations are: (i.) = 75, (ii.) = 50, (iii.) = 10, (iv.) = 10—making in all 145 ways of selecting the eight participants. 

A great many people will give the answer as 185, by overlooking the fact that in forty cases in class (iii.) precisely the same eight guests would be sharing the meal as in class (ii.), though the accommodating pair would be eating differently of the two dishes. 

This is the point that upset the calculations of the company.