Question

25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is

• A. 2
• B. 17
• C. 13
• D. 3

Answer 1

The correct option is D 3

Using the set theory formula,

n(A) : Number of people who play hockey = 15

n(B) : Number of people who play football = 17

n(A$\cap$B) : Persons who play both hockey and football = 10

n(A$\cup$B) : Persons who play either hockey or football or both

Using the formula,
n(A$\cup$B) = n(A) + n(B) -n(A$\cap$B)

n(A$\cup$B)=15 +17 -10 =22

Thus, people who play neither hockey nor football
= 25-22 = 3

Alternative Method

Refer to Venn diagram given below:

Number of people playing neither of the two games is equal to 3.