Question 975876: Please help me with this ..
In a a group of 60 students ..
34 are members of Music Club
30 are members of Art Club
32 are members of Math Club
25 are members of Art and Music Club
14 are members of Math and Music Club
11 are members of art and math
7 are members of all 3 Clubs
1.How many members in Math club only ?
2.How many members in Music Club only?
3.How many members in Art Club only ?
4.How many members in Art and Music but not members of Math Club?
5.How many are members of both math and music?
6.how many are not members of Math Club?
7.How many students do not belong to any of the three clubs ?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Two questions can be answered without much work:
5.How many are members of both math and music?
The problem says that " are members of Math and Music Club."
6.How many are not members of Math Club?
The problem says that
"In a a group of 60 students ... 32 are members of Math Club,"
so obviously  are not members of Math club.
Other questions require more work, and it is best to work with diagrams.
The diagram below shows that we know that
some students may not belong to any of the three clubs,
some students may belong to only one of the clubs,
some students may belong to two clubs,
and exactly 7 students belong to all three clubs.
 We can calculate some more facts and fill them into the diagram.
The group of 25 students who are members of Art and Music clubs includes those 7 students who belong to all three clubs.
It also includes
 students who belong to the Art and Music clubs, but not to the Math club. That is the answer to one of the questions:
4.How many members in Art and Music but not members of Math Club? 
The group of 14 students who are members of Math and Music clubs includes those 7 students who belong to all three clubs.
It also includes
 students who belong to the Math and Music clubs, but not to the Art club.
The group of 11 students who are members of Art and Math clubs includes those 7 students who belong to all three clubs.
It also includes
 students who belong to the Art and Math clubs, but not to the Music club.
So we re-draw the diagram with the calculated information:
 , and we calculate more and add the new calculations to the diagram.
 from the diagram we can answer some of the questions:
1.How many members in Math club only ?
2.How many members in Music Club only? 
3.How many members in Art Club only ? 
We have just one question left:
7.How many students do not belong to any of the three clubs ?
At this point, we can calculate how many of  students belong to one or more clubs:
32 belong to the Math club and maybe one or two other clubs,
2 belong to only the Music club,
1 student belongs to only the Art club,
and 18 students belong to both the Music and Art clubs.
So the total belonging to at least one club is
 .
Therefore, there must be  students that do not belong to any of the three clubs.
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