Posted by Debbi on .
11. In a survey of 260 dancers, 172 knew the ballroom dances, 145 knew the Latin dances, and 102 knew the swing dances. Of these, 65 knew the ballroom and swing dances, 93 knew the ballroom and Latin dances, and 56 knew the Latin and swing dances. Thirtyone dancers indicated that they knew all three styles of dance.
Create a Venn diagram to reflect the above data, label your diagram clearly and submit to the W1: Assignment 4 Dropbox. Use your diagram to answer the following questions here.
(a) How many knew only the ballroom dances?
(b) How many knew only the swing dances?
(c) How many knew exactly two of the three dances?
(d) How many knew the Latin and swing dances, but not the ballroom dances?
(e) How many knew none of these dances

Math 
DrRuss,
I'll get you started.
Draw three intersecting circles. Label one B, one S and one L.
From the data given we can place 31 in the intersection of all three.
We are told 65 knew the ballroom and swing dances, therefore the number that know ballromm and swing only is 6531=34
Similary the number that know swing and latin only is 5631=25
And the number that know latin and ballroom only is 9321=62.
Thus the number that know ballroom only is 172(34+31+62)=54
Thus the number that know swing only is 102(34+31+25)=12
Thus the number that know swing only is 145(25+31+62)=27
The number that knew two of the three dances is
62+34+25=121
How many knew the Latin and swing dances, but not the ballroom dances is
12+25+27=64
Total number that knew all three is
45+34+12+31+62+25+27=236
so the how many knew none of these dances is 260236=24
I hope this makes sense without a diagram. Please check the maths!