Question

There are 250 students taking band, chorus, or both. If there are 180 students taking band and 60 students in both band and chorus, how many students are only in chorus? (Hint: First find out how many students are only in band)

Answer 1

70 students are ONLY IN CHORUS.

Step-by-step explanation:

Total number of students taking either or both of the activities = 250

⇒n (B∪ C) = 250

Number of students taking band = n (B) = 180

So, the number of students taking Chorus = n (C)

Number of students taking both Band and Chorus = n (B ∪ C) = 60

Now, as we know n (B∪ C) = n (B ) + n (C) - n (B ∩ C)

⇒Here, 250 = 180 + n(C) - 60

or, n ( C) = 250 - 120 = 130

Hence, number of students taking Chorus = 130 = n (C)

Now, to find Students taking ONLY CHORUS:

Total Number of students in Chorus - Students In both Chorus and Band

or n ( C - B) = n (C) - n (B ∩ C)

= 130 - 60

= 70 , or n ( C - B) = 70

Hence, 70 students are ONLY IN CHORUS.