problem solving

Question

of 300 students, 110 are in the chorus and 150 are in the band.  Of these students, 50 are in both chorus and the band.  How many students are neither in the chorus nor the band?

Answer 1

Hi Brandon,

 

Total no of students = n( total students)= n(T)=300

No of students in Chorus= n( students in Chorus)=n(C)=110

No of students in band= n( band students) =n(B)=150

No of students in both chorus & the band= n(C & B both)=50

 

no of students in chorus or in Band= = n(C or B)=n(C)+n(B)-n(C&B)= 110+150-50=210

 

No of students neither in Chorus nor in Band= n(T)-n(C orB)=300-210=90

 

 

Meena from Strongsville ,OH

Answer 2

300 - (110 + 150 - 50) = 80

 

Total students - (Students in Chorus - Students in Band - Students in both)

 

Since 50 students are both in band and chorus there are double counted if we do 300 - (110 + 150). Hence we need to subtract 50 inside the parenthesis.