4. Seven pigeons each fly into one of nine pigeonholes. Determine how many possible pigeon configurations there are in each situation (a) - (d); explain your reasoning. (a) The pigeons are different colors, and may not share a hole; (b) The pigeons are different colors, and pigeons may share a hole; (c) The pigeons are the same color, and may not share a hole; (d) The pigeons are the same color, and may share a hole. (e) { extra credit - 1 point } Since there are nine pigeonholes, what is the minimum number of pigeons needed to guarantee that at least two pigeons share a pigeonhole, and why