<PRE><B>Question 433209</B>
I solve this type of problem by drawing
a Venn diagram and then I find how many
are in each little section of it.
B = ballroom
L = Latin
S = Swing
B and S but not other dances = 65 - 31 = 34
B and L but not other dances = 93 - 31 = 62
L and S but not other dances = 56 - 31 = 25
--------------
Now I can identify
B only = 172 - (34 + 62 + 31) = 45
L only = 145 - (62 + 31 + 25) = 27
S only = 102 - (34 + 31 + 25) = 12
--------------
(a) 45
(b) 12
(c) 34 + 62 + 25 = 121
(d) 25
(e) Counting each area only once,
45 + 27 + 12 + 34 + 62 + 25 + 31 = 236
260 - 236 = 24
 </PRE>