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Let X = {1, 2, 3} and Y = {a, b, c, d, e}. (1) How...

Let X = {1, 2, 3} and Y = {a, b, c, d, e}.

(1) How many functions f : X → Y are there?

(2) How many injective functions f : X → Y are there?

(3) What is a if (x + 2)10 = x 10 + · · · + ax7 + · · · + 512x + 1024?

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