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....

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

Accepted Answer

3 persons play neither hockey nor football. Answer: D. We have 25 people with overlapping sports preferences. Using the inclusion-exclusion principle, we find the count of people who play at least one sport, then subtract from the total to get those who play neither.

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