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  1. 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:

    2. A.
    2
    B.
    17
    C.
    13
    D.
    3

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    Answer : Option D

    Explanation :

    Representing the given information in the Venn diagrams, we have

    Let the number of people who play only hockey = a

    The number of people who play only football = b

    Now, a = n(H) - 10 = 15 - 10 = 5

    b = n(F) - 10 = 17 - 10 = 7

    Clearly, a + b + 10 + n = 25

    ⇒ n = 25 - 7 - 5 -10 ⇒ n = 3

    ∴ The number of people who do not play neither Hockey nor Football is 3.

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