New to discrete math. By[n] we mean {1,2,...n}. What is the number of monotone injective functions from [3] to [6]? I understand n choose k formula but it doesn't seem to solve the question. How do I change the calculation if the order between two sets are preserved? If anyone could provide some guidance on how to proceed, that would be great. Thanks!
2026-04-24 08:16:30.1777018590
How many monotone injective functions?
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There are $\binom{6}{3}=20$ ways to choose the $3$ different function values. In order to make the function monotone, we must arrange them in either increasing or decreasing order, so there are $40$ possible functions in all.
That is, either $f(1)<f(2)<f(3)$ or $f(1)>f(2)>f(3)$.