25 persons are in a room. 15 of them play hockey, 17 of them play football and…
2010
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
Attempted by 59 students.
Show answer & explanation
Correct answer: D
Solution: Use the inclusion-exclusion principle to find how many play at least one sport, then subtract from the total.
Number who play hockey or football = number who play hockey + number who play football - number who play both = 15 + 17 - 10 = 22.
Number who play neither = total persons - number who play hockey or football = 25 - 22 = 3.
Answer: 3 persons play neither hockey nor football.