Question

There are 30 students in a class. 10 students have a pet dog, 13 students have a pet cat, and 7 students have a pet fish. 4 students have both a pet dog and a pet cat, 6 students have a pet cat and a pet fish, 2 students have a pet dog and a pet fish. 1 student has all three. How many of the 30 students have pets?

Answer 1

9 students have pets

Explanation:

From the above question, we are given the following information

Total number of students = 30

Let Pet Dog = D

Pet Cat = C

Pet Fish = F

Number is students that have pet dog

(D) = 10 students

Number of students that have pet cat (C) = 13 students

Number of students that have pet fish (F) = 7 students

Number of students that have Pet dog and cat ( D and C) = 4 students

Number of students that have Pet cat and fish (C and F) = 6 students

Number of student that has pet dog and pet fish (D and F) = 2 students

1 student has all three = ( D and F and C)

Number of student that have a pet Dog only

= n(D) - [n( D and C) + n( D and F) - n(D and C and F)]

= 10 -( 4+ 2 -1)

= 10 - 5

= 5

Number of student that have Pet cat only

= n(C) -[ n( D and C) + n( C and F) - n( D and C and F)]

= 13 -( 4 + 6 - 1)

= 13 - 9

= 4

Number is student that have a pet fish only

= n(F) - [n (C and F) + n( D and F) - n( D and C and F)]

= 7 - [6 + 2 - 1]

= 7 - 7

= 0

The number of students that have pets is calculated as:

(Number of students that have dogs only + Number of student that have cats only + Number of students that have fish only)

= 5 + 4 + 0

= 9

Therefore only 9 students have pets.