Question

Consider the following problem: How many ways are there to paint 10 identical houses on a street with five colors if at most three houses can be painted blue, at most three can be painted green, at most three can be painted beige, and no constraint is placed on the other two colors, brown and gray? A student claims that the generating function for this problem is g(x) = (1 + x +x2 + r3)3(1 + x + r2 + +z'o)2 (a) Is the student correct? Why or why not? If the student is wrong, write the correct (b) Use a gencrating function to find the number of ways to paint 10 identical houses generating function given the restrictions

Answer 1

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