# Combinatorics

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

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)

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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.