In a class of 30 students, 10 take Mathematics, 15 take Physics, and 10 take neither. The number of students who take both mathematics and physics is

# In a class of 30 students, 10 take Mathematics, 15 take Physics, and 10 take neither. The number of students who take both mathematics and physics is 1. A

15

2. B

5

3. C

3

4. D

2

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### Solution:

Total number of students $n\left(\mu \right)=30$

$n\left(M\right)=10$

$n\left(P\right)=15$

$n\left(M\cup P\right)=30-10=20$

Let  $n\left(M\cap P\right)=x$

$n\left(M\cup P\right)=n\left(M\right)+n\left(P\right)-n\left(M\cap P\right)$

$20=10+15-x$

$x=5$

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