Answer: There are 7 students who want French only.
Step-by-step explanation:
Since we have given that
Number of students is planning schedules = 30
Number of students who want to take French = 16
Number of students who want to take Spanish = 16
Number of students want to take Latin = 11
Number of students who take both French and latin = 5-3 =2
Number of students who take French and Latin and Spanish as well = 3
Number of students who only want Latin = 5
Number of students who only want spanish = 8
According to venn diagram, we get that
[tex]a+b+g+f=16\\\\c+d+e+g=11\\\\b+e+f+g=16[/tex]
So, it becomes,
[tex]c+d+e+g=11\\\\5+2+e+3=11\\\\e=11-(5+2+3)=1[/tex]
Similarly,
[tex]b+e+f+g=16\\\\8+1+f+3=16\\\\12+e=16\\\\e=16-12\\\\e=4[/tex]
Similarly,
[tex]a+d+g+f=16\\\\a+2+3+4=16\\\\a=16-(2+3+4)\\\\a=16-9\\\\a=7[/tex]
Hence, there are 7 students who want French only.
