If there x number of objects, and y number of possible colors I can paint each of the objects. How do I count each unique permutation of objects and colors, e.g. A = { α, β, γ } and B = { red, orange, yellow, green, blue, indigo, violet }, then below is one permutation:
| red | orange | yellow | green | blue | indigo | violet |
α | | x | | | | | |
β | x | | | | | | |
γ | x | | | | | | |
and so on...
I know that counting permutations on a single dimension, i.e. the number of unique permutations of all the colors is 7!, and the number of permutations of colored objects if 3! in the given example.
How do I calculate the unique permutations of the two sets (object, colors)?
Is it simply the case that I should apply the binomial theorem as "y choose x". In our example: "1,000 colors, choose 3" - or is this incorrect?