Answer
The Venn diagram,
Work Step by Step
(a)
In the Venn diagram, the region VII represents the students participated only in campus sports. So, the required number of students is:
\[\begin{align}
& n\left( \text{only campus sports} \right)=n\left( \text{VII} \right) \\
& =30
\end{align}\]
(b)
In the Venn diagram, theregionVI represents the students participated in fraternities and sports, but not tutorial programs. So, the required number of students is:
\[\begin{align}
& n\left( \text{fraternities and sports, but not tutorial programs} \right)=n\left( \text{VI} \right) \\
& =8
\end{align}\]
(c)
In the Venn diagram, the sum of the regions V, VI and VII represent the students participated in fraternities or sports, but not tutorial programs. So, the required number of students is:
\[\begin{align}
& n\left( \text{classical or jazz, but not rock} \right)=n\left( \text{V} \right)+n\left( \text{VI} \right)+n\left( \text{VII} \right) \\
& =23+8+30 \\
& =61
\end{align}\]
(d)
In the Venn diagram, the sum of the regions I, V and VII represent the number of students listened to exactly one type of the musical styles. So, the required number of students is:
\[\begin{align}
& n\left( \text{exactly one style} \right)=n\left( \text{I} \right)+n\left( \text{V} \right)+n\left( \text{VII} \right) \\
& =14+23+30 \\
& =67
\end{align}\]
(e)
In the Venn diagram, the sum of the regions II, III, IV,and VI represent the number of students participated in at least two of these activities. So, the required number of students is:
\[\begin{align}
& n\left( \text{at least two styles} \right)=n\left( \text{II} \right)+n\left( \text{III} \right)+n\left( \text{IV} \right)+n\left( \text{VI} \right) \\
& =7+5+9+8 \\
& =29
\end{align}\]
(f)
In the Venn diagram, the region VIII representing the number of students whodid not participate in any of three activities is:
\[\begin{align}
& n\left( \text{none} \right)=n\left( \text{VIII} \right) \\
& =84
\end{align}\]
