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(a) Let there be a fixed m N. Find the EGF for the number of functions f : [n] [m] such that every j [m]

(a) Let there be a fixed m N. Find the EGF for the number of functions f : [n] [m] such that every j [m] has at least 3 pre-images. Write the EGF in terms of polynomials and exponentials (without any infinite sums).

(b) When m = 2, derive the formula for the exact number of such functions (without any summations).

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