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Question: a how many bijections are there from a 1...

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(a) How many bijections are there from A = {1, 2, 3, ..., 10} to itself? (b) How many invertible functions are there from A (as above) to B = {a, b, c, d, e, f, g, h, i, j}? (c) How many bijections are there from A to C = {a, b, c, d, e, f}? (d) How many invertible functions are there from A to B so that f(1) != a? (e) How many functions (not necessarily invertible) are there from A to C so f^ −1 ({c, d}) = {1, 2}? (f) How many functions (not necessarily invertible) are there from A to C so f ^−1 ({c, d}) = {1, 2, 3, 4}?

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