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    Exclamation number of elements



    & is divisible by 3.

    then the number of elements in the set S=?
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  2. #2
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    Quote Originally Posted by adhyeta View Post


    & is divisible by 3.

    then the number of elements in the set S=?
    Hi adhyeta.

    Let

    S_1=\{0,3,6,9\}
    S_2=\{1,4,7\}
    S_3=\{2,5,8\}

    Then there are four possibilities for a_1+a_2+a_3 to be divisible by 3:

    (a) a_1,a_2,a_3\in S_1. There are 4\times4\times4=64 choices for this.

    (b) a_1,a_2,a_3\in S_2. There are 3\times3\times3=27 choices here.

    (c) a_1,a_2,a_3\in S_3. Also 27 choices here.

    (d) a_1,a_2,a_3 belong to different S_1,S_2,S_3. Here there are 3!\times4\times3\times3=216 choices.

    So the total number of elements in S is 64+27+27+216=334.
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