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    Combinatorics

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    Problem1)
    What is the number of ways to color n objects with 3 colors if every color must be used at least once?

    problem2)
    prove that for any three sets A,B,C ;
    ((AB) U (BA))^ C = ((A^C) U (B^C)) (A^B^C) ^ means intersection

    Please explain the steps, help me understand.
    Thanks

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    https://brainmass.com/math/combinatorics/combinatorics-color-objects-168513

    Solution Preview

    Please see the attached file.

    problem1)
    What is the number of ways to color n objects with 3 colors if every color must be used at least once?

    problem2)
    prove that for any three sets A,B,C ;
    ((AB) U (BA))^ C = ((A^C) U (B^C)) (A^B^C) ^ means intersection

    Please explain the steps, help me understand.

    problem1)
    =======
    Let assume we have only two objects: Object1 and Object2; and three colors: C1, C2 an C3.
    Color of Object1 ...

    Solution Summary

    The expert determines what is the number of ways to color an object.

    $2.19