There were four
portions of warden pie and four
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.
combination must fall into one
the following groups.
(i.) Where the warden
pie is distributed entirely
among the five first mentioned;
(ii.) where only one of the
pair is given pie;
(iii.) where the other of the pair is given pie;
where both of the pair are given pie.
The numbers of
(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
the two dishes.
This is the point
that upset the calculations of the