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:

  1. A.

    2

  2. B.

    17

  3. C.

    13

  4. 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.

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