In a class of 100 students, there are 50 who play soccer, 45 who play
basketball, and 50 who play volleyball. Only 15 of these students play all
three sports. Everyone plays at least one of these sports. How many of
the students play exactly two of these sports? Choices.
A) 15
B) 20
C) 25
D) 30
E) 35
Let S1 be the number of students who play exactly one of the three sports; S2 - the   number of students who play exactly two of the three sports; and let S3 be the number   of students who play all three sports. We know that S3 = 15 and S1 + S2 + S3 = 100   (the total number of students). Also in the sum 50+45+50 (soccer players + basketball   players + volleyball players), each student who plays exactly one sport is counted once,   the ones who play exactly two sports are counted twice, and those who play all three   sports are counted three times. Thus, 50 + 45 + 50 = S1 + 2S2 + 3S3. Note that   S2 = (S1 + 2S2 + 3S3) − (S1 + S2 + S3) − 2S3 = 15   correct answer 15
<result>A</result>
In a class of 100 students, there are 50 who play soccer, 45 who play
basketball, and 50 who play volleyball. Only 15 of these students play all
three sports. Everyone plays at least one of these sports. How many of
the students play exactly two of these sports?