Question

In a survey of university students, 6464 had taken computer science and physics course, and 14 had taken all the three courses. Find the number of students who were surveyed. Find how many had taken one course only.

Answer 1

Let us represent the given data in a Venn diagram. Let M, C, P represent sets of students who had taken mathematics, computer science and physics respectively. The given details are filled in the Venn diagram
$n(M\cap C\cap P)=14$
$n(M\cap C\cap P^{\prime })=26-14=12$
$n(M\cap P\cap C^{\prime })=28-14=14$
$n(C\cap P\cap M^{\prime })=22-14=8$
Number of students surveyed
= 24 + 12 + 60 + 8 + 22 + 14 + 14 = 154
The number of students who had taken only mathematics $=64-(14+14+12)=24$
The number of students who had taken only computer science $=94-(12+14+8)=60$
The number of students who had taken only physics $=58-(14+14+8)=22$
The number of students who had taken one course only $=24+60+22=106$.