Question

In a class of 30 students in which at least one of them offered biology or physics, 17 offered physics, 16 offered both biology and physics. How many students offered physics only, biology only, only one subject, and how many offered neither?

A)Physics only: 1, Biology only: 0, Only one subject: 15, Neither: 14
B)Physics only: 17, Biology only: 0, Only one subject: 0, Neither: 13
C)Physics only: 1, Biology only: 0, Only one subject: 16, Neither: 13
D)Physics only: 17, Biology only: 0, Only one subject: 1, Neither: 11

Answer 1

To find the number of students who offered physics only, biology only, only one subject, and neither subject, we can use the principle of inclusion-exclusion.

Step-by-step explanation:

To find the number of students who offered physics only, biology only, only one subject, and neither subject, we can use the principle of inclusion-exclusion.

Let's denote the number of students who offered physics only as A, the number of students who offered biology only as B, and the number of students who offered both biology and physics as C.

We know that A + B + C represents the total number of students who offered either physics or biology. We also know that there are 30 students in total.

Using the given information, we can set up the following equations:

A + C = 17 (the number of students who offered physics)

B + C = 16 (the number of students who offered both biology and physics)

A + B + C = 30 (the total number of students)

By solving these equations, we find that A = 1, B = 0, and C = 15.

Therefore, the number of students who offered physics only is 1, biology only is 0, only one subject is 15, and neither subject is 14.